Question

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

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (B)

1

Answer 2

Here a+b=a–2,ab=–(a–1), Now,a²+b²=(a+b)²– 2ab

= (a– 2)² + 2 (a +1) = a² – 2a + 6 = (a–1)² + 5

So a² + b² will be maximum at a = 1.