TS EAMCET · Maths · Quadratic Equation
If \(\alpha, \beta, \gamma\) are the roots of the equation \(x^3+p x^2+q x+r=0\), then \((\alpha+\beta)(\beta+\gamma)(\gamma+\alpha)=\)
- A \(p-q r\)
- B \(r-p q\)
- C \(q-r p\)
- D \(r+p q\)
Answer & Solution
Correct Answer
(B) \(r-p q\)
Step-by-step Solution
Detailed explanation
We have, \[ x^3+p x^2+q x+r=0 \] \(\alpha, \beta, \gamma\) are roots of equation \[ \begin{aligned} \therefore \quad \alpha+\beta+\gamma & =-p \\ \alpha \beta+\beta \gamma+\alpha \gamma & =q \\ \alpha \beta \gamma & =-r \end{aligned} \] Now,…
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