# 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) **5x^{2} – 8x = -3(7 – 2x)

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

**(iv) **x^{2} + 5x – 5 = (x – 3)^{2}

**(v) **7x^{3} – 2x^{2} + 10 = (2x – 5)^{2}

**(vi) **(x – 1)^{2} + (x + 2)^{2} + 3(x +1) = 0

**Answer 1**

**(i)**

(3x – 1)^{2} = 5(x + 8)

⇒ (9x^{2} – 6x + 1) = 5x + 40

⇒ 9x^{2} – 11x – 39 =0; which is of the form ax^{2} + bx + c = 0.

∴ Given equation is a quadratic equation.

**(ii)**

5x^{2} – 8x = -3(7 – 2x)

⇒ 5x^{2} – 8x = 6x – 21

⇒ 5x^{2} – 14x + 21 =0; which is of the form ax^{2} + bx + c = 0.

∴ Given equation is a quadratic equation.

**(iii)**

(x – 4)(3x + 1) = (3x – 1)(x +2)

⇒ 3x^{2} + x – 12x – 4 = 3x^{2} + 6x – x – 2

⇒ 16x + 2 =0; which is not of the form ax^{2} + bx + c = 0.

∴ Given equation is not a quadratic equation.

**(iv) **

x^{2} + 5x – 5 = (x – 3)^{2}

⇒ x^{2} + 5x – 5 = x^{2} – 6x + 9

⇒ 11x – 14 =0; which is not of the form ax^{2} + bx + c = 0.

∴ Given equation is not a quadratic equation.

**(v) **

7x^{3} – 2x^{2} + 10 = (2x – 5)^{2}

⇒ 7x^{3} – 2x^{2} + 10 = 4x^{2} – 20x + 25

⇒ 7x^{3} – 6x^{2} + 20x – 15 = 0; which is not of the form ax^{2} + bx + c = 0.

∴ Given equation is not a quadratic equation.

**(vi)**

(x – 1)^{2} + (x + 2)^{2} + 3(x +1) = 0

⇒ x^{2} – 2x + 1 + x^{2} + 4x + 4 + 3x + 3 = 0

⇒ 2x^{2} + 5x + 8 = 0; which is of the form ax^{2} + bx + c = 0.

∴ Given equation is a quadratic equation.

#### Question 2

**(i) **Is x = 5 a solution of the quadratic equation x^{2} – 2x – 15 = 0?

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

#### Answer 2

**(i)**

x^{2} – 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 x^{2} – 2x – 15 = 0.

**(ii)**

2x^{2} – 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 2x^{2} – 7x + 9 = 0.

**Question 3**

If is a solution of equation 3x^{2} + 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 mx^{2} + nx + 6 = 0. Find the values of m and n.

**Answer 4**

**Question 5**

If 3 and -3 are the solutions of equation ax^{2} + bx – 9 = 0. Find the values of a and b.

**Answer 5**

** 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)7x^{2} – 9x +2 =0 (ii)6x^{2} – 13x +4 =0

(iii)25x^{2} – 10x +1=0 (iv)

(v)x^{2} – ax – b^{2} =0 (vi)2x^{2} +8x +9=0

**Answer 1**

#### Question 2

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

**Answer 2**

#### Question 3

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

x^{2} + (p – 3)x + p = 0

**Answer 3**

x^{2} + (p – 3)x + p = 0

Here, a = 1, b = (p – 3), c = p

Since, the roots are equal,

⇒ b^{2}– 4ac = 0

⇒ (p – 3)^{2}– 4(1)(p) = 0

⇒p^{2} + 9 – 6p – 4p = 0

⇒ p^{2}– 10p + 9 = 0

⇒p^{2}-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 3x^{2} – 12x + (n – 5)=0 has equal roots. Find the value of n.

**Answer 4**

#### Question 5

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

**Answer 5**

** **

**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

#### Question 2

Solve :

#### Answer 2

#### Question 3

Solve :

#### Answer 3

#### Question 4

Solve : x(x-5)= 24

#### Answer 4

#### Question 5

Solve :

#### Answer 5

#### Question 6

Solve :

#### Answer 6

#### Question 7

Solve :

#### Answer 7

#### Question 8

Solve :

#### Answer 8

#### Question 9

Solve :

#### Answer 9

#### Question 10

Solve :

#### Answer 10

#### Question 11

Solve :

#### Answer 11

#### Question 12

Solve :

#### Answer 12

#### Question 13

Solve :

#### Answer 13

#### Question 14

Solve :

#### Answer 14

#### Question 15

Solve :

#### Answer 15

#### Question 16

2x^{2} – 9x + 10 = 0, When

(i) x∈ N

(ii) x∈ Q

#### Answer 16

#### Question 17

Solve :

#### Answer 17

#### Question 18

Solve :

#### Answer 18

#### Question 19

Solve :

#### Answer 19

#### Question 20

Solve :

#### Answer 20

#### Question 21

Find the quadratic equation, whose solution set is :

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

#### Answer 21

#### Question 22

#### Answer 22

#### Question 23

#### Answer 23

#### Question 24

Find the value of x, if a + 1=0 and x^{2} + ax – 6 =0.

#### Answer 24

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

Put this value in the given equation x^{2} + ax – 6 =0

#### Question 25

Find the value of x, if a + 7=0; b + 10=0 and 12x^{2} = 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

#### 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

#### Question 27

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

#### Answer 27

Consider the equation, 6x^{2} – 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 x^{2} – 3x +2=0

or not.

#### Answer 28

x^{2} – 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 7x^{2}+mx – 3=0;

Find the value of m.

#### Answer 29

7x^{2}+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^{2 }+ 7x + n = 0, find the values of m and n.

#### Answer 30

#### Question 31

If quadratic equation x^{2} – (m + 1) x + 6=0 has one root as x =3;

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

#### Answer 31

#### Question 32

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

#### Answer 32

#### Question 33

#### Answer 33

or x = -(a + b)

#### Question 34

#### Answer 34

#### Question 35

If -1 and 3 are the roots of x^{2}+px+q=0

then find the values of p and q

#### Answer 35

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

#### Question 1

Solve each of the following equations using the formula :

(i)x^{2} – 6x =27 (ii)x^{2} – 10x +21=0

(iii)x^{2} +6x – 10 =0 (iv)x^{2} +2x – 6=0

(v)3x^{2}+ 2x – 1=0 (vi)2x^{2} + 7x +5 =0

(vii) (viii)

(ix) (x)

(xi) (xii)

(xiii) (xiv)

#### Answer 1

#### Question 2

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

(i)x^{2} – 8x+5=0

(ii)5x^{2} +10x – 3 =0

#### Answer 2

#### Question 3

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

(i)2x^{2} – 10x +5=0

(ii)

(iii) x^{2} – 3x – 9 =0

(iv) x^{2} – 5x – 10 = 0

#### Answer 3

(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)3x^{2} – 12x – 1 =0

(ii)x^{2} – 16 x +6= 0

(iii)2x^{2} + 11x + 4= 0

#### Answer 4

#### Question 5

Solve:

(i)x^{4} – 2x^{2} – 3 =0

(ii)x^{4} – 10x^{2} +9 =0

#### Answer 5

#### Question 6

Solve :

(i)(x^{2} – x)^{2} + 5(x^{2} – x)+ 4=0

(ii)(x^{2} – 3x)^{2} – 16(x^{2} – 3x) – 36 =0

#### Answer 6

#### Question 7

Solve :

(i)

(ii)

(iii)

#### Answer 7

#### Question 8

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

#### Answer 8

#### 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

#### Question 11

Solve the quadratic equation x^{2} – 3(x + 3)=0 ; Give your answer correct to two significant figures.

#### Answer 11

x^{2} – 3(x + 3)=0

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

**Exercise – 5(E)**

#### Question 1

Solve:

#### Answer 1

#### Question 2

Solve: (2x+3)^{2}=81

#### Answer 2

#### Question 3

#### Answer 3

#### Question 4

#### Answer 4

#### Question 5

#### Answer 5

#### Question 6

#### Answer 6

#### Question 7

#### Answer 7

#### Question 8

#### Answer 8

#### Question 9

#### Answer 9

#### Question 10

#### Answer 10

#### Question 11

#### Answer 11

#### Question 12

Solve each of the following equations, giving answer upto two decimal places.(i)x^{2} – 5x -10=0(ii) 3x^{2} – x – 7 =0

#### Answer 12

#### Question 13

#### Answer 13

#### Question 14

Solve :

(i)x^{2} – 11x – 12 =0; when x ∈N

(ii)x^{2} – 4x – 12 =0; when x∈ I

(iii)2x^{2} – 9x + 10 =0; when x∈Q

#### Answer 14

#### Question 15

#### Answer 15

#### Question 16

#### Answer 16

#### Question 17

#### Answer 17

#### Question 18

#### Answer 18

#### Question 19

#### Answer 19

#### 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:

** **

** **

**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)

(ii)

(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

#### Question 3

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

#### Answer 3

#### Question 4

If and ;find the values of x.

#### Answer 4

#### **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

#### Question 9

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

#### Answer 9

#### Question 10

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

#### Answer 10

#### Question 11

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

#### Answer 11

#### Question 12

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

(i)

(ii)

#### Answer 12

#### Question 13

Solve :

(i) and x > 0.

(ii) and x < 0.

#### Answer 13

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

** **

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