AP EAMCET · Maths · Quadratic Equation
If \(\alpha, \beta\) and \(\gamma\) are the roots of the equation \(x^3-a^2+b x-c\) \(=0\) then, \(\alpha^{-2}+\beta^{-2}+\gamma^{-2}=\)
- A \(\frac{b^2-3 a c}{c^2}\)
- B \(\frac{b^2-a c}{c^2}\)
- C \(\frac{\mathrm{b}^2-2 \mathrm{ac}}{\mathrm{c}^2}\)
- D \(\frac{b^2-4 a c}{e^2}\)
Answer & Solution
Correct Answer
(C) \(\frac{\mathrm{b}^2-2 \mathrm{ac}}{\mathrm{c}^2}\)
Step-by-step Solution
Detailed explanation
Since \(\alpha, \beta, \gamma\) are the roots of the equation \(\begin{aligned} & x^3-a x^2+b x-c=0 \\ & \therefore \alpha+\beta+\gamma=\mathrm{a} \\ & \alpha \beta+\beta \gamma+\gamma \alpha=\mathrm{b} \\ & \alpha \beta \gamma=\mathrm{c}\end{aligned}\) Now,…
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