AP EAMCET · Maths · Quadratic Equation
If \(\alpha, \beta\) and \(\gamma\) are roots of the equation \(x^3+4 x-19=0\). Then, the value of \(\frac{\alpha^3}{19-4 \alpha}+\frac{\beta^3}{19-4 \beta}+\frac{\gamma^3}{19-4 \gamma}\) is equal to
- A 0
- B 3
- C -3
- D 2
Answer & Solution
Correct Answer
(B) 3
Step-by-step Solution
Detailed explanation
\(\alpha, \beta\) and \(\gamma\) are roots of \(x^3+4 x-19=0\) Then, \(\alpha+\beta+\gamma=0\) \(\begin{aligned} \alpha \beta+\beta \gamma+\gamma \alpha & =4 \\ \alpha \beta \gamma & =19\end{aligned}\) \[ \alpha \beta \gamma=19 \] From Eq. (ii),…
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