AP EAMCET · Maths · Quadratic Equation
The cubic equation whose roots are the squares of the roots of \(x^3-2 x^2+10 x-8=0\), is
- A \(x^3+16 x^2+68 x-64=0\)
- B \(x^3+8 x^2+68 x-64=0\)
- C \(x^3+16 x^2-68 x-64=0\)
- D \(x^3-16 x^2+68 x-64=0\)
Answer & Solution
Correct Answer
(A) \(x^3+16 x^2+68 x-64=0\)
Step-by-step Solution
Detailed explanation
Let, \(\alpha, \beta\) and \(\gamma\) are the roots of \[ \begin{aligned} & x^3-2 x^2+10 x-8 & =0 \\ \therefore & \alpha+\beta+\gamma & =2, \end{aligned} \] \[ \alpha \beta+\beta \gamma+\gamma \alpha=10 \] and \(\alpha \beta \gamma=8\) Now, \(\alpha^2+\beta^2+\gamma^2\)…
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