JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If \(\alpha\) and \(\beta\) are the distinct roots of the equation \(x^{2}+(3)^{1 / 4} x+3^{1 / 2}=0\), then the value of \(\alpha^{96}\left(\alpha^{12}-\right.1) +\beta^{96}\left(\beta^{12}-1\right)\) is equal to:
- A \(56 \times 3^{25}\)
- B \(52 \times 3^{24}\)
- C \(56 \times 3^{24}\)
- D \(28 \times 3^{25}\)
Answer & Solution
Correct Answer
(B) \(52 \times 3^{24}\)
Step-by-step Solution
Detailed explanation
As, \(\left(a^{2}+\sqrt{3}\right)=-(3)^{1 / 4} \cdot \alpha\) \(\Rightarrow\left(\alpha^{2}+2 \sqrt{3} \alpha^{2}+3\right)=\sqrt{3} \alpha^{2} \text { (On squaring) }\) \(\left.\therefore\left(a^{4}+3\right)=(-) \sqrt{3} \alpha^{2}\right)\)…
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