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Question: The values of 'a' for which the sum of roots of the equation $x^2+(2-a-a^2)x-a^2=0$ is zero are $\al...

The values of 'a' for which the sum of roots of the equation x2+(2−a−a2)x−a2=0x^2+(2-a-a^2)x-a^2=0 is zero are α\alpha and β\beta then ∣α+β∣=|\alpha + \beta|=

A

1

B

3

C

5

D

7

Answer

1

Explanation

Solution

For the quadratic equation x2+Bx+C=0x^2+Bx+C=0, the sum of the roots is −B-B. In this case, the sum of the roots is −(2−a−a2)=a2+a−2-(2-a-a^2) = a^2+a-2. We are given that the sum of the roots is zero, so a2+a−2=0a^2+a-2=0. Factoring this quadratic in 'a', we get (a+2)(a−1)=0(a+2)(a-1)=0. The values of 'a' are α=−2\alpha = -2 and β=1\beta = 1 (or vice versa). We need to find ∣α+β∣=∣−2+1∣=∣−1∣=1|\alpha + \beta| = |-2 + 1| = |-1| = 1.