JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let \(\alpha, \beta\) be the roots of the equation \(x^2-x+2=0\) with \(\operatorname{Im}(\alpha)>\operatorname{Im}(\beta)\). Then \(\alpha^6+\alpha^4+\beta^4-5 \alpha^2\) is equal to
- A \(45\)
- B \(47\)
- C \(13\)
- D \(36\)
Answer & Solution
Correct Answer
(C) \(13\)
Step-by-step Solution
Detailed explanation
\(\alpha^6+\alpha^4+\beta^4-5 \alpha^2 \) \( =\alpha^4(\alpha-2)+\alpha^4-5 \alpha^2+(\beta-2)^2 \) \( =\alpha^5-\alpha^4-5 \alpha^2+\beta^2-4 \beta+4 \) \( =\alpha^3(\alpha-2)-\alpha^4-5 \alpha^2+\beta-2-4 \beta+4 \) \( =-2 \alpha^3-5 \alpha^2-3 \beta+2 \)…
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