RD Sharma Solutions for Class 10 Maths Chapter 8 Quadratic Equations Exercise 8.5

A method commonly called the Quadratic formula is the main focus of this exercise. It’s also known as the Shreedharacharya’s rule. This method overcomes certain limitations of the factorization method. For a detailed study regarding this concept, students can refer to the RD Sharma Solutions Class 10 prepared by experts at BYJU’S. The RD Sharma Solutions for Class 10 Maths Chapter 8 Quadratic Equations Exercise 8.5 PDF is provided below.

RD Sharma Solutions for Class 10 Maths Chapter 8 Quadratic Equations Exercise 8.5

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Access RD Sharma Solutions for Class 10 Maths Chapter 8 Quadratic Equations Exercise 8.5

1. Write the discriminant of the following quadratic equations:

(i) 2x2 – 5x + 3 = 0

Solution:

Given equation,

2x2 – 5x + 3 = 0

It is in the form of ax2 + bx + c = 0

Where, a = 2, b = -5 and c = 3

So, the discriminant is given by D = b2 – 4ac

D = (-5)2 – 4 x 2 x 3

D = 25 – 24 = 1

Hence, the discriminant of the given quadratic equation is 1.

(ii) x2 + 2x + 4 = 0

Solution:

Given equation,

x2 + 2x + 4 = 0

It is in the form of ax2 + bx + c = 0

Where, a = 1, b = 2 and c = 4

So, the discriminant is given by D = b2 – 4ac

D = (2)2 – 4 x 1 x 4

D = 4 – 16 = – 12

Hence, the discriminant of the given quadratic equation is – 12.

(iii) (x – 1)(2x – 1) = 0

Solution:

Given equation,

(x -1) (2x -1) = 0

On expanding it, we get

2x2 – 3x + 1 = 0

It is in the form of ax2 + bx + c = 0

Where, a = 2, b = -3, c = 1

So, the discriminant is given by D = b2 – 4ac

D = (-3)2 – 4 x 2 x 1

D = 9 – 8 = 1

Hence, the discriminant of the given quadratic equation is 1.

(iv) x2 -2x + k = 0, k ∈ R

Solution:

Given equation,

x– 2x + k = 0

It is in the form of ax2 + bx + c = 0

Where, a = 1, b = -2, and c = k

So, the discriminant is given by D = b2 – 4ac

D = (-2)2 – 4(1)(k)

= 4 – 4k

Hence, the discriminant of the given equation is (4 – 4k).

R D Sharma Solutions For Class 10 Maths Chapter 8 Quadratic Equations ex 8.5 - 1

(v)

Solution:

R D Sharma Solutions For Class 10 Maths Chapter 8 Quadratic Equations ex 8.5 - 2

(vi) x2 – x + 1 = 0

Solution:

Given equation,

x2 – x + 1 = 0 It is in the form of ax2 + bx + c = 0

Where, a = 1, b = -1 and c = 1

So, the discriminant is given by D = b2 – 4ac

D = (-1)2 – 4 × 1 × 1

D = 1 – 4 = – 3

Thus, the discriminant of the given equation is -3.

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