AP EAMCET · Maths · Quadratic Equation
If \(\alpha\) and \(\beta\) are the roots of \(x^2-2 x+4=0\), then the value of \(\alpha^6+\beta^6\) is
- A 32
- B 64
- C 128
- D 256
Answer & Solution
Correct Answer
(C) 128
Step-by-step Solution
Detailed explanation
Given, \(\alpha, \beta\) are the roots of \(x^2-2 x+4=0\) \(\alpha+\beta=2 ...(i)\) \(\alpha \beta=4 ...(ii)\) Now, \(\begin{aligned} \alpha-\beta & =\sqrt{(\alpha+\beta)^2-4 \alpha \beta} \\ & =\sqrt{4-4 \times 4}=\sqrt{-12} \end{aligned}\)…
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