AP EAMCET · Maths · Quadratic Equation
If \(\alpha, \beta, \gamma\) are the roots of the equation \(x^3-a x^2+b x-c=0\), then \(\Sigma \alpha^2(\beta+\gamma)=\)
- A \(a b-3 c\)
- B \(\frac{a b-3 c}{c}\)
- C \(\frac{b^2-2 a c}{c^2}\)
- D \(\frac{a^2-2 b}{c^2}\)
Answer & Solution
Correct Answer
(A) \(a b-3 c\)
Step-by-step Solution
Detailed explanation
If \(\alpha, \beta, \gamma\) are the roots of the equation. \[ x^3-a x^2+b x-c=0 \] Then, \(\alpha+\beta+\gamma=a, \alpha \beta+\beta \gamma+\gamma \alpha=b\) and \(\alpha \beta \gamma=c\). Now, \(\Sigma \alpha^2(\beta+\gamma)=\Sigma \alpha^2(a-\alpha)\) [as…
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