JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let \(\alpha\) and \(\beta\) be the roots of the equation \(5 x^{2}+6 x-2=0 .\) If \(S_{n}=\alpha^{n}+\beta^{n}, n=1,2,3 \ldots\) then :
- A \(5 \mathrm{S}_{6}+6 \mathrm{S}_{5}=2 \mathrm{S}_{4}\)
- B \(5 \mathrm{S}_{6}+6 \mathrm{S}_{5}+2 \mathrm{S}_{4}=0\)
- C \(6 \mathrm{S}_{6}+5 \mathrm{S}_{5}+2 \mathrm{S}_{4}=0\)
- D \(6 \mathrm{S}_{6}+5 \mathrm{S}_{5}=2 \mathrm{S}_{4}\)
Answer & Solution
Correct Answer
(A) \(5 \mathrm{S}_{6}+6 \mathrm{S}_{5}=2 \mathrm{S}_{4}\)
Step-by-step Solution
Detailed explanation
\(\alpha\) and \(\beta\) are roots of \(5 x^{2}+6 x-2=0\) \(\Rightarrow 5 \alpha^{2}+6 \alpha-2=0\) \(\Rightarrow 5 \alpha^{n+2}+6 \alpha^{n+1}-2 \alpha^{n}=0 \quad \ldots(1)\) (By multiplying \(\left.\alpha^{n}\right)\) Similarly…
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