WBJEE · Maths · Quadratic Equation
The value of a for which sum of the squares of the roots of the equation \(x^2-(a-2) x-a-1=0\) assumes the least value is
- A 0
- B 1
- C 2
- D 3
Answer & Solution
Correct Answer
(B) 1
Step-by-step Solution
Detailed explanation
Let \(\alpha, \beta\) be the roots, then \(\begin{aligned} &\alpha^2+\beta^2=(\alpha+\beta)^2-2 \alpha \beta \\ &=(a-2)^2+2(a+1) \\ &=a^2-2 a+6 \\ &=(a-1)^2+5 \geq 5 \\ &\therefore \alpha^2+\beta^2 \text { is minimum if } a=1 . \end{aligned}\)
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