AP EAMCET · Maths · Quadratic Equation
If \(\alpha, \beta, \gamma\) are the roots of \(x^3+p x^2+q x+r=0\), then the value of \(\left(1+\alpha^2\right)\left(1+\beta^2\right)\left(1+\gamma^2\right)\) is
- A \((r-p)^2+(r-q)^2\)
- B \((1+p)^2+(1+q)^2\)
- C \((r+p)^2+(q+1)^2\)
- D \((r-p)^2+(q-1)^2\)
Answer & Solution
Correct Answer
(D) \((r-p)^2+(q-1)^2\)
Step-by-step Solution
Detailed explanation
Given that \(\alpha, \beta\) and \(\gamma\) are the roots of the equation \(x^3+p x^2+q x+r=0\) \(\alpha+\beta+\gamma=-p ...(i)\) \(\alpha \beta+\beta \gamma+\gamma \alpha=q ...\) and \(\alpha \beta \gamma=-r ...(iii)\)…
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