AP EAMCET · Maths · Quadratic Equation
If \(\alpha, \beta\) and \(\gamma\) are the roots of the equation \(x^3-3 x^2+x+5=0\), then \(y=\Sigma \alpha^2+\alpha \beta \gamma\) satisfies the equation
- A \(y^3+y+2=0\)
- B \(y^3-y^2-y-2=0\)
- C \(y^3+3 y^2-y-3=0\)
- D \(y^3+4 y^2+5 y+20=0\)
Answer & Solution
Correct Answer
(B) \(y^3-y^2-y-2=0\)
Step-by-step Solution
Detailed explanation
Given, \(\alpha, \beta\) and \(\gamma\) are roots of \(x^3-3 x^2+x+5=0\) \(\therefore \quad \alpha+\beta+\gamma=3\) \(\alpha \beta+\beta \gamma+\gamma \alpha=1\) \(\alpha \beta \gamma=-5\) Now, \(y=\Sigma \alpha^2+\alpha \beta \gamma\)…
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