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

RD Sharma Class 10 Solutions Chapter 8 Ex 8.5 PDF Free Download

One another method commonly called as the Quadratic formula is the main focus in this exercise. Its also known as the Shreedharacharya’s rule. This method overcomes certain limitations of the factorization method. For detailed study regarding this concept, students can refer 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 Chapter 8 Quadratic Equations Exercise 8.5 Download PDF

RD Sharma Solutions for Class 10 Chapter 8 Quadratic Equations Exercise 8.5 29
RD Sharma Solutions for Class 10 Chapter 8 Quadratic Equations Exercise 8.5 30

Access RD Sharma Solutions for Class 10 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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