Question

The value of 'a' for which the sum of the squares of the roots of 2x² – 2(a – 2)x – a – 1 = 0 is least is ______.

पर्याय

• 1

• `3/2`

• 2

• –1

Answer 1

The value of 'a' for which the sum of the squares of the roots of 2x² – 2(a – 2)x – a – 1 = 0 is least is `underlinebb(3/2)`.

Explanation:

Let y = α² + β² = (α + β)² – 2αβ

y = `((2("a" - 2))/2)^2 + (2("a" + 1))/2`

y = a² – 3a + 5

= `("a" - 3/2)^2 + 11/4`

⇒ y is minimum, when

a = `3/2`