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
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,
x2 – 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).
(v)
Solution:
(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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