Question

If α and β are the zeros of x^2 + (k^2 – 1)x – 20, such that α^2 – β^2 – αβ = 29 and α – β = 9 then, the value of k is _______

(a) 1

(b) 0

(c) 2

(d) 3

I have been asked this question during an online exam.

This is a very interesting question from Zeros and Coefficients of Polynomial in division Polynomials of Mathematics – Class 10

Answer 1

The correct option is (b) 0

Explanation: α and β are the zeros of x^2 + (k^2 – 1)x – 20

So, α + β = -(k^2 – 1) and αβ = -20

Also, α – β = 9

Now, α^2 – β^2 – αβ = -11

(α + β)(α – β) – αβ = 29

-(k^2 – 1)9 + 20 = 29

-(k^2 – 1)9 = 9

-(k^2 – 1) = 1

(k^2 – 1) = -1

k^2 = -1 + 1

k = 0