Concise Solutions Quadratic Equations Chapter 5 ICSE Maths

Concise Solutions Quadratic Equations Chapter 5 for ICSE Maths Class 10 is available here. All Solution of Concise of Chapter 5 Quadratic Equations in One Variable has been solved according instruction given by council. This is the  Solution of Chapter-5 Quadratic Equation in one variable for ICSE Class 10th .ICSE Maths text book of Concise is In series of famous ICSE writer in maths. Concise is most famous among students. With the help of Concise solution student can achieve their goal in 2020 exam of council.

Concise Solutions Quadratic Equations Chapter 5 for ICSE Maths Class 10

The Solution of Concise Mathematics Chapter 5 Quadratic Equations for ICSE Class 10  have been solved by experience teachers from across the globe  to help students of class 10th  ICSE board exams conducted by the ICSE (Indian Council of Secondary Education) board papering in 2020. Therefore the ICSE Class 10th Maths Solutions of Concise solve problems of exercise and Chapter test related to various topics which are prescribed in most ICSE Maths textbooks.

  Chapter- 5 ,Quadratic Equations “Concise Maths Solutions” Select Topics

Exe – 5(A)Exe- 5(B) Exe- 5(C)Exe 5(D)Exe 5(E)Exe 5(F)

How to Solve Concise Solutions Quadratic Equations

Note:- Before viewing Solutions of Chapter -5 Quadratic  Equations of Concise Maths  read the Chapter Carefully then solve all example of your text book. The Chapter- 5 Quadratic Equations is main Chapter in ICSE board .     

Solutions of Concise Maths Chapter 5 – Quadratic Equations Exercise-5(A)

Exercise- 5(A)

Question 1

 Find which of the following equation are quadrants.

(i)  (3x – 1)2 = 5(x + 8)

(ii) 5x2 – 8x = -3(7 – 2x)

(iii) (x – 4)(3x + 1) = (3x – 1)(x +2)

(iv) x2 + 5x – 5 = (x – 3)2

(v) 7x3 – 2x2 + 10 = (2x – 5)2

(vi) (x – 1)2 + (x + 2)2 + 3(x +1) = 0

Answer 1

(i)

(3x – 1)2 = 5(x + 8)

⇒ (9x2 – 6x + 1) = 5x + 40

⇒ 9x2 – 11x – 39 =0; which is of the form ax2 + bx + c = 0.

∴ Given equation is a quadratic equation.

(ii)

5x2 – 8x = -3(7 – 2x)

⇒ 5x2 – 8x = 6x – 21

⇒ 5x2 – 14x + 21 =0; which is of the form ax2 + bx + c = 0.

∴ Given equation is a quadratic equation.

(iii)

(x – 4)(3x + 1) = (3x – 1)(x +2)

⇒ 3x2 + x – 12x – 4 = 3x2 + 6x – x – 2

⇒ 16x + 2 =0; which is not of the form ax2 + bx + c = 0.

∴ Given equation is not a quadratic equation.

(iv) 

x2 + 5x – 5 = (x – 3)2

⇒ x2 + 5x – 5 = x2 – 6x + 9

⇒ 11x – 14 =0; which is not of the form ax2 + bx + c = 0.

∴ Given equation is not a quadratic equation.

(v) 

7x3 – 2x2 + 10 = (2x – 5)2

⇒ 7x3 – 2x2 + 10 = 4x2 – 20x + 25

⇒ 7x3 – 6x2 + 20x – 15 = 0; which is not of the form ax2 + bx + c = 0.

∴ Given equation is not a quadratic equation.

(vi)

(x – 1)2 + (x + 2)2 + 3(x +1) = 0

⇒ x2 – 2x + 1 + x2 + 4x + 4 + 3x + 3 = 0

⇒ 2x2 + 5x + 8 = 0; which is of the form ax2 + bx + c = 0.

∴ Given equation is a quadratic equation.

Question 2

(i) Is x = 5 a solution of the quadratic equation x2 – 2x – 15 = 0?

(ii) Is x = -3 a solution of the quadratic equation 2x2 – 7x + 9 = 0?

Answer 2

(i)

x2 – 2x – 15 = 0

For x = 5 to be solution of the given quadratic equation it should satisfy the equation.

So, substituting x = 5 in the given equation, we get

L.H.S = (5)2 – 2(5) – 15

= 25 – 10 – 15

and = 0

hence = R.H.S

Hence, x = 5 is a solution of the quadratic equation x2 – 2x – 15 = 0.

(ii)

2x2 – 7x + 9 = 0

For x = -3 to be solution of the given quadratic equation it should satisfy the equation

So, substituting x = 5 in the given equation, we get

L.H.S=2(-3)2 – 7(-3) + 9

 = 18 + 21 + 9

 = 48

 ≠ R.H.S

Hence, x = -3 is not a solution of the quadratic equation 2x2 – 7x + 9 = 0.

Question 3

If   is a solution of equation 3x2 + mx + 2 = 0, find the value of m.

Answer 3

For x = √2/√3  to be solution of the given quadratic equation it should satisfy the equation

So, substituting x = √2/√3 in the given equation, we get

Question 4 

  and 1 are the solutions of equation mx2 + nx + 6 = 0. Find the values of m and n.

Answer 4

Ans 4 EXe(a) CONCISE

Question 5

If 3 and -3 are the solutions of equation ax2 + bx – 9 = 0. Find the values of a and b.

Answer 5

Ans 5 Exe 5 (A) Concise

 Quadratic Equations Chapter- 5 Concise Solutions Exercise – 5(B) for ICSE Maths Class 10 

Exercise – 5(B)

Question 1 

Without solving, comment upon the nature of roots of each of the following equations :

(i)7x2 – 9x +2 =0 (ii)6x2 – 13x +4 =0

(iii)25x2 – 10x +1=0 (iv)

(v)x2 – ax – b2 =0 (vi)2x2 +8x +9=0

Answer 1

Ans 1(i) exe5(b) Selina

Ans 1(i) EXE5(a) Concise

Question 2

Find the value of p, if the following quadratic equation has equal roots : 4x2 – (p – 2)x + 1 = 0

Answer 2

Ans 2 exe5(b) Concise

Question 3

Find the value of ‘p’, if the following quadratic equations have equal roots :

x2 + (p – 3)x + p = 0

Answer 3

x2 + (p – 3)x + p = 0

 Here, a = 1, b = (p – 3), c = p

 Since, the roots are equal,

⇒ b2– 4ac = 0

⇒ (p – 3)2– 4(1)(p) = 0

⇒p2 + 9 – 6p – 4p = 0

⇒ p2– 10p + 9 = 0

⇒p2-9p – p + 9 = 0

⇒p(p – 9) – 1(p – 9) = 0

⇒ (p -9)(p – 1) = 0

⇒ p – 9 = 0 or p – 1 = 0

⇒ p = 9 or p = 1

Question 4

The equation 3x2 – 12x + (n – 5)=0 has equal roots. Find the value of n.

Answer 4

Ans 4 exe5(b) concise

Question 5

Find the value of m, if the following equation has equal roots : (m – 2)x2 – (5+m)x +16 =0

Answer 5

Ans 5 exe5(b) concise

 

Exercise-5(C) ,Chapter 5 – Quadratic Equations Concise Maths Solutions for ICSE Maths Class 10th

Exercise  5(C)

Solve equation, number 1 to 20 given below using factorization method:

Question 1

Solve :  x²-10x-24 = 0

Answer 1

Ans 1 5(c) Concise

Question 2

Solve :

Answer 2

Ans2 5(c) Concise

Question 3

Solve :

Answer 3

Ans 3 5(c) Concise

Question 4

Solve : x(x-5)= 24

Answer 4

Ans 4 5(c) concise

Question 5

Solve :

Answer 5

Ans 5 5(c) concise

Question 6

Solve :

Answer 6

Ans 6 5(c) Concise

Question 7

Solve :

Answer 7

Ans 7 5(c) concise

Question 8

Solve :

Answer 8

Ans 8 5(c) Concise

Question 9

Solve :

Answer 9

Ans 9 5(c) concise

Question 10

Solve :

Answer 10

Ans 10 5(c) concise

Question 11

Solve :

Answer 11

Ans 11 5(c) concise

Question 12

Solve :

Answer 12

Ans 12 5(c) concise

Question 13

Solve :

Answer 13

Ans 13 5(c) concise

Question 14

Solve :

Answer 14

Ans 14 5(c) concise

Question 15

Solve :

Answer 15

Ans 15 5(c) concise

Question 16

2x2 – 9x + 10 = 0, When

(i) x∈ N

(ii) x∈ Q

Answer 16

Ans 16 5(c) concise

Question 17

Solve :

Answer 17

Ans 17 5(c) concise

Question 18

Solve :

Answer 18

Ans 18 5(c) concise

Question 19

Solve :

Answer 19

Ans 19 5(c) concise

Question 20

Solve :

Answer 20

Answer 20 5(c) concise

Question 21

Find the quadratic equation, whose solution set is :

(i) {3, 5} (ii) {-2, 3}

Answer 21

Ans 21 5(c) concise

Question 22

Answer 22

Ans 22 5(c) concise

Question 23

Que 23 5(c) concise

Answer 23

Ans 23 5(c) concise

Question 24

Find the value of x, if a + 1=0 and x2 + ax – 6 =0.

Answer 24

If a+1=0, then a = -1

Put this value in the given equation x2 + ax – 6 =0

Ans 24 5(c) concise

Question 25

Find the value of x, if a + 7=0; b + 10=0 and 12x2 = ax – b.

Answer 25

If a + 7 =0, then a = -7

and b + 10 =0, then b = – 10

Put these values of a and b in the given equation

Ans 25 5(c) concise

Question 26

Use the substitution y= 2x +3 to solve for x, if 4(2x+3)2 – (2x+3) – 14 =0.

Answer 26

4(2x+3)2 – (2x+3) – 14 =0

Put 2x+3 = y

Ans 26 5(c) concise

Question 27

Without solving the quadratic equation 6x2 – x – 2=0, find whether  x equals 2 over 3  is a solution of this equation or not.

Answer 27

Consider the equation, 6x2 – x – 2=0

Put x equals 2 over 3in L.H.S.

Ans 27 5(c) concise

Since L.H.S.= R.H.S., then x equals 2 over 3    is a solution of the given equation.

Question 28

Determine whether x = -1 is a root of the equation x2 – 3x +2=0

or not.

Answer 28

x2 – 3x +2=0

Put x = -1 in L.H.S.

L.H.S. = (-1)2 – 3(-1) +2

= 1 +3 +2=6  ≠R.H.S.

Then x = -1 is not the solution of the given equation.

Question 29

If x =  2/3is a solution of the quadratic equation 7x2+mx – 3=0;

Find the value of m.

Answer 29

7x2+mx – 3=0

Given x =2/3  is the solution of the given equation.

Put given value of x in the given equation

 

Question 30

If x = -3 and x = 2/3 are solutions of quadratic equation mx+ 7x + n = 0, find the values of m and n.

Answer 30

Ans 30 5(c) concise

Question 31

If quadratic equation x2 – (m + 1) x + 6=0 has one root as x =3;

find the value of m and the root of the equation.

Answer 31

Ans 31 5(c) concise

Question 32

Given that 2 is a root of the equation 3x2 – p(x + 1) = 0 and that the equation px2 – qx + 9 = 0 has equal roots, find the values of p and q.

Answer 32

Ans 32 5(c) concise

Question 33

Que 33 5(c) concise

Answer 33

or x = -(a + b)

Question 34

Que 34 5(c) concise

Answer 34

Ans 34 5(c) concise

Question 35

If -1 and 3 are the roots of x2+px+q=0
then find the values of p and q

Answer 35

Ans 35 5(c) concise

ICSE Concise Solutions Quadratic Equations Exercise – 5(D) Chapter-5

Question 1

Solve each of the following equations using the formula :

(i)x2 – 6x =27 (ii)x2 – 10x +21=0

 

(iii)x2 +6x – 10 =0 (iv)x2 +2x – 6=0

 

(v)3x2+ 2x – 1=0 (vi)2x2 + 7x +5 =0

 

(vii)         (viii)

(ix)              (x)

(xi)               (xii)

(xiii)         (xiv)

Answer 1

Ans 1 5(d) concise

Ans 1 i 5(d) concise

Ans 1 ii 5(d) concise

Ans 1 iii 5(d) concise

Ans 1 iv 5(d) concise

Question 2

Solve each of the following equations for x and give, in each case, your answer correct to one decimal place :

(i)x2 – 8x+5=0

(ii)5x2 +10x – 3 =0

Answer 2

Ans 2 5(d) concise

Question 3

Solve each of the following equations for x and give, in each case, your answer correct to two decimal places :

(i)2x2 – 10x +5=0

(ii)

(iii) x2 – 3x – 9 =0

(iv) x2 – 5x – 10 = 0

Answer 3

(i)

(ii)

(iii)

(iv)

Ans 3 5(d) concise

Question 4

Solve each of the following equations for x and give, in each case, your answer correct to 3 decimal places :

(i)3x2 – 12x – 1 =0

(ii)x2 – 16 x +6= 0

(iii)2x2 + 11x + 4= 0

Answer 4

Ans 7 5(d)concise

Question 5

Solve:

(i)x4 – 2x2 – 3 =0

(ii)x4 – 10x2 +9 =0

Answer 5

Ans 8 5(d) concise

Question 6

Solve :

(i)(x2 – x)2 + 5(x2 – x)+ 4=0

(ii)(x2 – 3x)2 – 16(x2 – 3x) – 36 =0

Answer 6

Ans 9 5(d) concise

Question 7

Solve :

(i)

(ii)

(iii)

Answer 7

Ans 10 5(d) concise

Ans 10 (ii) 5(d) concise

Ans 10 iii 5(d) concise

Question 8

Solve the equation .  2x- 1/x= 7. Write your answer correct to two decimal places.

Answer 8

Ans 11 5(d) concise

Question 9

Solve the following equation and give your answer correct to 3 significant figures:

Answer 9

Consider the given equation:

Question 10

Solve for x using the quadratic formula. Write your answer correct to two significant figures.

(x – 1)2 – 3x + 4 = 0

Answer 10

Ans 13 5(d) concise

Question 11

Solve the quadratic equation x2 – 3(x + 3)=0 ; Give your answer correct to two significant figures.

Answer 11

x2 – 3(x + 3)=0

Ans 14 5(d) concise

 Concise Solution Quadratic Equations Chapter -5 Exercise 5(E) 

Exercise – 5(E)

Question 1

Solve:

Answer 1

Ans 2 5(e) concise

Question 2

Solve: (2x+3)2=81

Answer 2

Ans 2 i 5(e) concise

Question 3

Que 3 5(e) concise

Answer 3

Ans 3 5(e) concise

Question 4

Answer 4

Ans 4 5(e) concise

Question 5

begin mathsize 11px style straight x space plus space 4 over straight x space equals space minus 4 semicolon space straight x space not equal to 0 end style

Answer 5

Question 6

Answer 6

Ans 6 5(e) concise

Question 7

Answer 7

Question 8

Answer 8

Ans 8 5(e) concise

Question 9

Answer 9

Ans 9 5 (e) concise

Question 10

Answer 10

Ans 10 5(e) concise

Question 11

Answer 11

Ans 11 5 (e) concise

Question 12

Solve each of the following equations, giving answer upto two decimal places.(i)x2 – 5x -10=0(ii) 3x2 – x – 7 =0

Answer 12

Question 13

Answer 13

Ans 13 5(e) concise

Question 14

Solve :

(i)x2 – 11x – 12 =0; when x ∈N

(ii)x2 – 4x – 12 =0; when x∈ I

(iii)2x2 – 9x + 10 =0; when x∈Q

Answer 14

Ans 14 5 (e) concise

Question 15

Answer 15

Ans 15 5(e) concise

Question 16

Answer 16

Ans 16 5(e) concise

Question 17

Que 17 5(e) concise

Answer 17

Ans 17 5(e) concise

Question 18

Answer 18

Ans 18 i5(e) c0ncise

Ans 18 ii5(e) concise

Question 19

Answer 19

Ans 19 5(e) concise

Question 20

Without solving the following quadratic equation, find the value of ‘m’ for which the given equation has real and equal roots.

Answer 20

Consider the given equation:

Ans 20 5(e) concise

 

Chapter 5 – Quadratic Equations Exercise -5(F) Concise Solutions for ICSE Maths Class 10th

Exercise -5 (F)

Question 1

Solve :

(i) (x+5)(x-5)=24

(ii)

(iii)

Answer 1

(i)Ans 1 5(f) concise

 (ii)Ans 1 ii5(f) concise

 (iii)

Question 2

One root of the quadratic equation             is    . Find the value of m. Also, find the other root of the equation

Answer 2

Ans 2 5(f) concise

Question 3

One root of the quadratic equation           is -3, find its other root.

Answer 3

Ans 3 5(f)

Question 4

If    and   ;find the values of x.

Answer 4

Ans 4 5(f)

 Question 5   

 

 update Soon 

Answer 5

Question 6

If m and n are roots of the equation  where x ≠ 0 and x ≠ 2; find m × n.

Answer 6

Given quadratic equation is

Since, m and n are roots of the equation, we have

   and

Hence,

Question 7

Solve, using formula :

Answer 7

Given quadratic equation is

Using quadratic formula,

⇒ x = a + 1 or x = -a – 2 = -(a + 2)

 

Question 8

Solve the quadratic equation

(i) When   (integers)

(ii) When  (rational numbers)

Answer 8

Ans 7 5(f)

Question 9

Find the value of m for which the equation                 has real and equal roots.

Answer 9

Ans 8 5(f)

Question 10

Find the values of m for which equation                  has equal roots. Also, find the roots of the given equation.

Answer 10

Ans 9 5(f)

Question 11

Find the value of k for which equation   has real roots.

Answer 11

Ans 10 5 (f)

Question 12

Find, using quadratic formula, the roots of the following quadratic equations, if they exist

(i)

(ii) 

Answer 12

Ans 11 5(f)

Question 13

Solve :

(i)      and x > 0.

(ii)    and x < 0.

Answer 13

Ans 12

—-: End of Concise Solutions Quadratic Equations Chapter 5   :——

 

Chapter Wise Concise Maths Solution for ICSE Class 10th

  1. Goods and Service tax (GST)
  2. Banking
  3. Shares and Dividends
  4. Linear In equations
  5. Quadratic Equations in One Variable
  6. Factorization
  7. Ratio and Proportion
  8. Matrices
  9. Arithmetic and Geometric Progression
  10. Reflection
  11. Section formula
  12. Equation of Straight Line
  13. Similarity
  14. Locus
  15. Circles
  16. Constructions
  17. Mensuration
  18. Trigonometric Identities
  19. Trigonometric Tables
  20. Heights and Distances
  21. Measures of Central Tendency
  22. Probability

Other Subject Chapter-Wise Solution for ICSE

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