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 \((\alpha+\beta-2 \gamma)(\beta+\gamma-2 \alpha)(\gamma+\alpha-2 \beta)=\)
- A \(2 a^3+9 a b+27 c\)
- B \(2 a^3+9 a b-27 c\)
- C \(2 a^3-9 a b+27 c\)
- D \(2 a^3-9 a b-27 c\)
Answer & Solution
Correct Answer
(C) \(2 a^3-9 a b+27 c\)
Step-by-step Solution
Detailed explanation
\(\alpha+\beta+\gamma = -a\) \(\alpha+\beta-2\gamma = (\alpha+\beta+\gamma)-3\gamma = -a-3\gamma\) \(\beta+\gamma-2\alpha = (\alpha+\beta+\gamma)-3\alpha = -a-3\alpha\) \(\gamma+\alpha-2\beta = (\alpha+\beta+\gamma)-3\beta = -a-3\beta\)…
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