# R S Aggarwal Solutions for Class 10 Maths Chapter 4 Quadratic Equations Exercise 4C

The set of R S Aggarwal Solutions is a useful study material for students to practice on various Maths concepts and clear their doubts. Students can download free pdf of class 10 Maths Chapter 4 Quadratic Equations exercise 4C by clicking on the given link below. This exercise concept helps students solve quadratic equations using the quadratic formula which is also known as Shridharacharyaâ€™s Rule and nature of quadratic equations roots using discriminant.

## Download PDF of R S Aggarwal Solutions for Class 10 Maths Chapter 4 Quadratic Equations Exercise 4C

### Access Other Exercise solutions of Maths R S Aggarwal Class 10 Chapter 4 – Quadratic EquationsÂ

Exercise 4A Solutions: 30 Questions (Short Answers)

Exercise 4B Solutions: 16 Questions (Short Answers)

Exercise 4D Solutions: 20 Questions (Long Answers)

## Exercise 4C Page No: 191

Find the discriminant of each of the following equations:

Question 1:

(i) 2xÂ² â€“ 7x + 6 = 0

(ii) 3xÂ² â€“ 2x + 8 = 0

(iii) 2xÂ² â€“ 5âˆš2x + 4 = 0

(iv) âˆš3 xÂ² + 2âˆš2 x â€“ 2âˆš3 =0

(v) (x â€“ 1) (2x â€“ 1) = 0

(vi) 1 â€“ x = 2xÂ²

Solution:

(i) 2xÂ² â€“ 7x + 6 = 0

Compare given equation with the general form of quadratic equation, which is

ax^2 + bx + c = 0

Here, a = 2, b = -7 and c = 6

Discriminant formula: D = b^2 – 4ac

(-7)^2 – 4 x 2 x 6

= 1

(ii) 3xÂ² â€“ 2x + 8 = 0

Compare given equation with the general form of quadratic equation, which is ax^2 + bx + c = 0

Here, a = 3, b = â€“ 2, c = 8

Discriminant formula: D = b^2 – 4ac

= (â€“ 2)^2 â€“ 4.3.8

= 4 â€“ 96

= â€“ 92

(iii) 2xÂ² â€“ 5âˆš2x + 4 = 0

Compare given equation with the general form of quadratic equation, which is ax^2 + bx + c = 0

Here, a = 2, b = â€“ 5âˆš2, c = 4

Discriminant formula: D = b^2 – 4ac

= (â€“ 5âˆš2)^2 â€“ 4.2.4

= 50 – 32

= 18

(iv) âˆš3 xÂ² + 2âˆš2 x â€“ 2âˆš3 =0

Compare given equation with the general form of quadratic equation, which is ax^2 + bx + c = 0

Here, a = âˆš3, b = 2âˆš2, c = â€“ 2âˆš3

Discriminant formula: D = b^2 – 4ac

= (2âˆš2)^2 â€“ 4(âˆš3)(â€“ 2âˆš3)

= 32

(v) (x â€“ 1) (2x â€“ 1) = 0

2x^2 â€“ 3x + 1 = 0

Compare given equation with the general form of quadratic equation, which is ax^2 + bx + c = 0

Here, a = 2, b = -3, c = â€“1

Discriminant formula: D = b^2 – 4ac

= (-3)^2 â€“ 4x2x1

= 1

(vi) 1 â€“ x = 2xÂ²

1 â€“ x = 2xÂ²

2x^2 + x â€“ 1 = 0

Compare given equation with the general form of quadratic equation, which is ax^2 + bx + c = 0

Here, a = 2, b = 1, c = â€“1

Discriminant formula: D = b^2 – 4ac

= (1)^2 â€“ 4x2x-1

= 9

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

Question 2:

xÂ² â€“ 4x â€“ 1 = 0

Solution:

xÂ² â€“ 4x â€“ 1 = 0

Compare given equation with the general form of quadratic equation, which is ax^2 + bx + c = 0

Here, a = 1, b = -4, c = â€“1

Find Discriminant:

D = b^2 – 4ac

= (-4)^2 â€“ 4x1x-1

= 20 > 0

$\large x = \frac{-b\pm \sqrt{D}}{2a}$

Therefore, x = 2 + âˆš5 and x = 2 – âˆš5

Question 3:

xÂ² â€“ 6x + 4 = 0

Solution:

Compare given equation with the general form of quadratic equation, which is ax^2 + bx + c = 0

a = 1, b = -6, c = 4

Find Discriminant:

D = b^2 – 4ac

= (-6)^2 â€“ 4.1.4

= 36 – 16

= 20 > 0

Roots of equation are real.

Find the Roots:

$\large x = \frac{-b\pm \sqrt{D}}{2a}$

x = 3 + âˆš5 or x = 3 â€“ âˆš5

Question 4:

2xÂ² + x â€“ 4 = 0

Solution:

Compare given equation with the general form of quadratic equation, which is ax^2 + bx + c = 0

a = 2, b = 1, c = -4

Find Discriminant:

D = b^2 – 4ac

= (1)^2 â€“ 4.2.-4

= 1 + 32

= 33 > 0

Roots of equation are real.

$\large x = \frac{-b\pm \sqrt{D}}{2a}$

Question 5:

25xÂ² + 30x + 7 = 0

Solution:

25xÂ² + 30x + 7 = 0

Compare given equation with the general form of quadratic equation, which is ax^2 + bx + c = 0

a = 25, b = 30, c = 7

Find Discriminant:

D = b^2 – 4ac

= (30)^2 â€“ 4.25.7

= 900 â€“ 700

= 200 > 0

Roots of equation are real.

Find the Roots:

$\large x = \frac{-b\pm \sqrt{D}}{2a}$

Question 6:

16xÂ² = 24x + 1

Solution:

16xÂ² – 24x â€“ 1 =0

Compare given equation with the general form of quadratic equation, which is ax^2 + bx + c = 0

a = 16 , b = -24, c = -1

Find Discriminant:

D = b^2 – 4ac

= (-24)^2 â€“ 4.16.-1

= 576 + 64

= 640 > 0

Roots of equation are real.

$\large x = \frac{-b\pm \sqrt{D}}{2a}$

Question 7:

15xÂ² â€“ 28 = x

Solution:

15xÂ² -x â€“ 28 = 0

Compare given equation with the general form of quadratic equation, which is ax^2 + bx + c = 0

a = 15, b =-1 , c = -28

Find Discriminant:

D = b^2 – 4ac

= (-1)^2 â€“ 4.15.(-28)

= 1 + 1680

= 1681 > 0

Roots of equation are real.

$\large x = \frac{-b\pm \sqrt{D}}{2a}$

X = 7/5 or x = -4/3

Question 8:

2xÂ² â€“ 2âˆš2 x + 1 = 0

Solution:

2xÂ² â€“ 2âˆš2 x + 1 = 0

Compare given equation with the general form of quadratic equation, which is ax^2 + bx + c = 0

a = 2, b = â€“ 2âˆš2, c = 1

Find Discriminant:

D = b^2 – 4ac

= (â€“ 2âˆš2)^2 â€“ 4.2.1

= 8 – 8

= 0

Equation has equal root.

Find roots:

$\large x = \frac{-b\pm \sqrt{D}}{2a}$

x = 1/âˆš2 or x = 1/âˆš2

Roots of equation are real.

Question 9:

âˆš2 xÂ² + 7x + 5âˆš2 = 0

Solution:

âˆš2 xÂ² + 7x + 5âˆš2 = 0

Compare given equation with the general form of quadratic equation, which is ax^2 + bx + c = 0

a = âˆš2 , b = 7 , c = 5âˆš2

Find Discriminant:

D = b^2 – 4ac

= (7)^2 â€“ 4. âˆš2 . 5âˆš2

= 49 – 40

= 9> 0

Roots of equation are real.

Find roots:

$\large x = \frac{-b\pm \sqrt{D}}{2a}$

Roots are:

x = – âˆš2 or x = -5/âˆš2

Question 10:

âˆš3 xÂ² + 10x â€“ 8âˆš3 = 0

Solution:

âˆš3 xÂ² + 10x â€“ 8âˆš3 = 0

Compare given equation with the general form of quadratic equation, which is ax^2 + bx + c = 0

a = âˆš3, b = 10 , c = â€“ 8âˆš3

Find Discriminant:

D = b^2 – 4ac

= (10)^2 â€“ 4. âˆš3 . â€“ 8âˆš3

= 100 + 96

= 196 > 0

Roots of equation are real.

Find roots:

$\large x = \frac{-b\pm \sqrt{D}}{2a}$

Roots are:

x = 2âˆš3/3 or x = -4âˆš3

Question 11:

âˆš3 xÂ² â€“ 2âˆš2 x â€“ 2âˆš3 = 0

Solution:

âˆš3 xÂ² â€“ 2âˆš2 x â€“ 2âˆš3 = 0

Compare given equation with the general form of quadratic equation, which is ax^2 + bx + c = 0

a = âˆš3 , b = â€“ 2âˆš2, c = â€“ 2âˆš3

Find Discriminant:

D = b^2 – 4ac

= (â€“ 2âˆš2)^2 â€“ 4. âˆš3 . â€“ 2âˆš3

= 8 + 24

= 32 > 0

Roots of equation are real.

Find roots:

$\large x = \frac{-b\pm \sqrt{D}}{2a}$

x = âˆš6 or x = -âˆš2/âˆš3

Question 12:

2xÂ² + 6âˆš3 x â€“ 60 = 0

Solution:

2xÂ² + 6âˆš3 x â€“ 60 = 0

Compare given equation with the general form of quadratic equation, which is ax^2 + bx + c = 0

a = 2, b = 6âˆš3, c = â€“ 60

Find Discriminant:

D = b^2 – 4ac

= (6âˆš3)^2 â€“ 4.2. â€“ 60

= 108 + 480

= 588 > 0

Roots of equation are real.

Find roots:

$\large x = \frac{-b\pm \sqrt{D}}{2a}$

Question 13:

4âˆš3 xÂ² + 5x â€“ 2âˆš3 = 0

Solution:

4âˆš3 xÂ² + 5x â€“ 2âˆš3 = 0

Compare given equation with the general form of quadratic equation, which is ax^2 + bx + c = 0

a = 4âˆš3 , b = 5, c = â€“ 2âˆš3

Find Discriminant:

D = b^2 – 4ac

= (5)^2 â€“ 4. 4âˆš3 . â€“ 2âˆš3

= 25 + 96

= 121 > 0

Roots of equation are real.

Find roots:

$\large x = \frac{-b\pm \sqrt{D}}{2a}$

Roots are:

x = âˆš3/4 or x = -2/âˆš3

Question 14:

3xÂ² â€“ 2âˆš6 x + 2 = 0

Solution:

3xÂ² â€“ 2âˆš6 x + 2 = 0

Compare given equation with the general form of quadratic equation, which is ax^2 + bx + c = 0

a = 3, b = â€“ 2âˆš6 , c = 2

Find Discriminant:

D = b^2 – 4ac

= (â€“ 2âˆš6)^2 â€“ 4. 3 . 2

= 24 – 24

= 0

Roots of equation are equal.

Find roots:

$\large x = \frac{-b\pm \sqrt{D}}{2a}$

Roots are:

x = âˆš2/âˆš3 and x = x = âˆš2/âˆš3

Question 15:

2âˆš3 xÂ² â€“ 5x + âˆš3 = 0

Solution:

2âˆš3 xÂ² â€“ 5x + âˆš3 = 0

Compare given equation with the general form of quadratic equation, which is ax^2 + bx + c = 0

a = 2âˆš3, b = â€“ 5 , c = âˆš3

Find Discriminant:

D = b^2 – 4ac

= (â€“ 5)^2 â€“ 4. 2âˆš3 . âˆš3

= 25 – 24

= 1 > 0

Roots of equation are real.

Find roots:

$\large x = \frac{-b\pm \sqrt{D}}{2a}$

Roots are:

x = âˆš3/2 and x = 1/âˆš3

## R S Aggarwal Solutions for Class 10 Maths Chapter 4 Quadratic Equations Exercise 4C

Class 10 Maths Chapter 4 Quadratic Equations Exercise 4C is based on the topics: