TS EAMCET · Maths · Quadratic Equation
If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2+2 x+2=0\), then \(\alpha^{15}+\beta^{15}=\)
- A \(-512\)
- B \(-256\)
- C \(256\)
- D \(512\)
Answer & Solution
Correct Answer
(B) \(-256\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & x^2+2 x+2=0 \\ & x= \frac{-2 \pm \sqrt{4-8}}{2}=\frac{-2 \pm 2 i}{2} \\ & x=-1 \pm i, \alpha=-1+i, \beta=-1-i \\ & \alpha^{15}+\beta^{15}=(-1+i)^{15}+(-1-i)^{15} \\…
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