﻿ The real values of a for which the sum of the squares of the roots of the equation x2 – (a – 2) x – a – 1 = 0 assume the least value is : Kaysons Education

# The Real Values Of a for Which The Sum Of The Squares Of The Roots Of The Equation x2 – (a – 2) x – a – 1 = 0 Assume The Least Value Is

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## Question

### Solution

Correct option is

1

Discriminant of the equation is (a – 2)2 + 4(a + 1)

= a2 – 4a + 4 + 4a + 4

= a2 + 8 > 0 as a Ïµ R.

∴ Roots of the given equation are real. Let these roots be α and β

Then α + β = a – 2, αβ = – (α + 1).

We have

α2 + β 2 = (α + β)2 - 2αβ = (α - 2)2 + 2 (α + 1)

= a2 – 4a + 4 + 2a + 2 = a2 – 2a + 6

= (a – 1)2 + 5

Thus, α2 + β 2 is least when a =1.

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