WBJEE · Maths · Quadratic Equation
For what value of ' \(a\) ', the sum of the squares of the roots of the equation \(x^2-(a-2) x-a+1=0\) will have the least value?
- A \(2\)
- B \(0\)
- C \(3\)
- D \(1\)
Answer & Solution
Correct Answer
(D) \(1\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \alpha^2+\beta^2=(\alpha+\beta)^2-2 \alpha \beta \\ & =(a-2)^2-2(1-a) \\ & =a^2-4 a+4-2+2 a \\ & =a^2-2 a+2 \\ & =(a-1)^2+1\end{aligned}\)
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