AP EAMCET · Maths · Quadratic Equation
If one root of the equation \(x^3-6 x^2+3 x+10=0\) is the average of the other two, then the sum of fourth powers of the roots of the equation is
- A \(642\)
- B \(643\)
- C \(644\)
- D \(645\)
Answer & Solution
Correct Answer
(A) \(642\)
Step-by-step Solution
Detailed explanation
Let \(\alpha, \beta\) and \(\gamma\) are the roots of \(x^3-6 x^2+3 x+10=0\) Also, let \(\beta=\frac{\alpha+\gamma}{2} \Rightarrow 2 \beta=\alpha+\gamma\) \(\therefore \alpha+2+\gamma=6 \Rightarrow \alpha+\gamma=4\) ...(i) Also,…
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