TS EAMCET · Maths · Quadratic Equation
If \(\alpha, \beta\) and \(\gamma\) are the roots of the equation \(x^3+p x^2+q x+r=0\), then the coefficient of \(x\) in the cubic equation whose roots are \(\alpha(\beta+\gamma), \beta(\gamma+\alpha)\) and \(\gamma(\alpha+\beta)\) is
- A \(2 q\)
- B \(q^2+p r\)
- C \(p^2-q r\)
- D \(r(p q-r)\)
Answer & Solution
Correct Answer
(B) \(q^2+p r\)
Step-by-step Solution
Detailed explanation
Since, \(\alpha, \beta\) and \(\gamma\) are the roots of \(f(x)=x^3+p x^2+q x+r=0\). \(\therefore \quad \alpha+\beta+\gamma=-p, \quad \alpha \beta+\beta \gamma+\gamma \alpha=q\) and \(\alpha \beta \gamma=-r\) Let…
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