Question
Mathematics Question on Quadratic Equations
The minimum value of the sum of the squares of the roots of x2 + (3 – a)x + 1 = 2a is
A
4
B
5
C
6
D
8
Answer
6
Explanation
Solution
The correct answer is (C) : 6
Fig.
α + β = a – 3, αβ = 1 – 2a
⇒ α2 + β2 = (a – 3)2 – 2(1– 2a)
= a2 – 6a + 9 – 2 + 4a
= a2 – 2a + 7
= (a – 1)2 + 6
So,
α2 + β2 ≥ 6