Question

If the sum of the squares of the roots of the equation x2 - (a - 2x - (a + 1) = 0 is least, then the value of a is (a) - 1 (b) 1 (c) 2 (d) -2​

Answer 1

Answer:

b) 1

Explanation:

Let roots are α and β

from the equation α + β = a − 2, αβ = −(a+1)

α² + β² = (α+β)² − 2αβ

α² + β² = (a−2)² + 2(a+1)=a² − 2a + 6

We have to find minimum value of a

a² − 2a + 6

⇒a² − 2a +1 + 5

⇒(a−1)² + 5

as least value of (a−1)² is zero ⇒a − 1= 0

Therefore, for least value a = 1

Hence, option 'B' is correct.