TS EAMCET · Maths · Quadratic Equation
Suppose \(\alpha, \beta, \gamma \quad\) are roots of \(x^3+x^2+2 x+3=0\). If \(f(x)=0\) is a cubic polynomial equation whose roots are \(\alpha+\beta, \beta+\gamma, \gamma+\alpha\), then \(f(x)\) is equal to
- A \(x^3+2 x^2-3 x-1\)
- B \(x^3+2 x^2-3 x+1\)
- C \(x^3+2 x^2+3 x-1\)
- D \(x^3+2 x^2+3 x+1\)
Answer & Solution
Correct Answer
(C) \(x^3+2 x^2+3 x-1\)
Step-by-step Solution
Detailed explanation
Given, the roots of \(x^3+x^2+2 x+3=0\) are \(\alpha, \beta\) and \(\gamma\). \[ \therefore \] \[ \begin{aligned} \alpha+\beta+\gamma & =-1 \\ \alpha \beta+\beta \gamma+\gamma \alpha & =2 \end{aligned} \] and \[ \alpha \beta \gamma=-3 \] and…
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