WBJEE · Maths · Quadratic Equation
If \(\alpha, \beta\) are the roots of the quadratic equation \(x^{2}+p x+q=0,\) then the values of \(\alpha^{3}+\beta^{3}\) and \(\alpha^{4}+\alpha^{3} \beta^{2}+\beta^{4}\) are respectively
- A \(3 p q-p^{3}\) and \(p^{4}-3 p^{2} q+3 q^{2}\)
- B \(-p\left(3 q-p^{2}\right)\) and \(\left(p^{2}-q\right)\left(p^{2}+3 q\right)\)
- C \(p q-4\) and \(p^{4}-q^{4}\)
- D \(3 p q-p^{3}\) and \(\left(p^{2}-q\right)\left(p^{2}-3 q\right)\)
Answer & Solution
Correct Answer
(D) \(3 p q-p^{3}\) and \(\left(p^{2}-q\right)\left(p^{2}-3 q\right)\)
Step-by-step Solution
Detailed explanation
\(\because\) Sum of roots, \(\alpha+\beta=-p\) and \(\alpha \beta=q\) \(\therefore \quad\left(a^{3}+\beta^{3}\right)=(\alpha+\beta)^{3}-3 \alpha \beta(\alpha+\beta)\)…
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