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CGP EDU Academic Team
Published on: August 14, 2026
The value of ‘a’ so that the sum of the squares of the roots of the equation x 2 – (a – 2) x – a + 1 = 0. assume the least value, is
Text Solution
Verified by ExpertsThe correct answer is:
D
x 2 – (a – 2) x – a + 1 = 0
α + β = (a – 2), αβ = 1 – a
α 2 + β 2 = ( α + β ) 2 – 2 αβ = (a – 2) 2 – 2 (1 – a)
= a 2 – 4a + 4 – 2 + 2a = a 2 – 2a + 2
= (a – 1) 2 + 1
It is minimum when a = 1
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