TS EAMCET · Maths · Quadratic Equation
If \(\alpha, \beta, \gamma\) are roots of \(x^3-5 x+4=0\), then \(\left(\alpha^3+\beta^3+\gamma^3\right)^2\) is equal to
- A 12
- B 13
- C 169
- D 144
Answer & Solution
Correct Answer
(D) 144
Step-by-step Solution
Detailed explanation
Given, the roots of \[ \begin{array}{rlrl} & & x^3-5 x+4 & =0 \text { are } \alpha \beta \text { and } \gamma \\ \therefore & \alpha+\beta+\gamma & =0 \end{array} \] Since, \[ \alpha \beta+\beta \gamma+\gamma \alpha=5 \text { and } \alpha \beta \gamma=-4 \] \(\therefore\)…
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