# 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(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)

#### 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

(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?

(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.

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.

#### Question 5

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

### 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

#### Question 2

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

#### Question 3

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

x2 + (p – 3)x + p = 0

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.

#### Question 5

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

### 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

Solve :

Solve :

#### Question 4

Solve : x(x-5)= 24

Solve :

Solve :

Solve :

Solve :

Solve :

Solve :

Solve :

Solve :

Solve :

Solve :

Solve :

#### Question 16

2x2 – 9x + 10 = 0, When

(i) x∈ N

(ii) x∈ Q

Solve :

Solve :

Solve :

Solve :

#### Question 21

Find the quadratic equation, whose solution set is :

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

#### Question 24

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

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

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

#### Question 25

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

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

#### Question 26

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

4(2x+3)2 – (2x+3) – 14 =0

Put 2x+3 = y

#### Question 27

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

Consider the equation, 6x2 – x – 2=0

Put in L.H.S.

Since L.H.S.= R.H.S., then     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.

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.

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.

#### 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.

#### 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.

or x = -(a + b)

#### Question 35

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

### 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)

#### 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

#### 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

(i)

(ii)

(iii)

(iv)

#### 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

#### Question 5

Solve:

(i)x4 – 2x2 – 3 =0

(ii)x4 – 10x2 +9 =0

#### Question 6

Solve :

(i)(x2 – x)2 + 5(x2 – x)+ 4=0

(ii)(x2 – 3x)2 – 16(x2 – 3x) – 36 =0

Solve :

(i)

(ii)

(iii)

#### Question 8

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

#### Question 9

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

Consider the given equation:

#### Question 10

(x – 1)2 – 3x + 4 = 0

#### Question 11

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

x2 – 3(x + 3)=0

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

Exercise – 5(E)

Solve:

#### Question 2

Solve: (2x+3)2=81

#### Question 12

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

#### 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

#### Question 20

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

Consider the given equation:

### 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)

(i)

(ii)

(iii)

#### Question 2

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

#### Question 3

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

#### Question 4

If    and  ;find the values of x.

update Soon

#### Question 6

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

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

and

Hence,

#### Question 7

Solve, using formula :

⇒ x = a + 1 or x = -a – 2 = -(a + 2)

#### Question 8

(i) When  (integers)

(ii) When (rational numbers)

#### Question 9

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

#### Question 10

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

#### Question 11

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

#### Question 12

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

(i)

(ii)

#### Question 13

Solve :

(i)     and x > 0.

(ii)   and x < 0.