TS EAMCET · Maths · Quadratic Equation
If the cubic equation \(x^3-a x^2+a x-1=0\) is identical with the cubic equation whose roots are the squares of the roots of the given cubic equation, then the non-zero real value of ' \(a\) ' is
- A \(\frac{1}{2}\)
- B 2
- C 3
- D \(\frac{7}{2}\)
Answer & Solution
Correct Answer
(C) 3
Step-by-step Solution
Detailed explanation
Let \(\alpha, \beta, \gamma\) are roots of equation \[ \begin{aligned} x^3-a x^2+a x-1 & =0 \\ \alpha+\beta+\gamma & =a \\ \alpha \beta+\beta \gamma+\alpha \gamma & =a \\ \alpha \beta \gamma & =-1 \end{aligned} \] Cubic equation whose roots are \(\alpha^2, \beta^2, \gamma^2\) is…
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