JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let \(\alpha, \beta(\alpha>\beta)\) be the roots of the quadratic equation \(x ^{2}- x -4=0\). If \(P _{ a }=\alpha^{ n }-\beta^{ n }, n \in N\), then \(\frac{ P _{15} P _{16}- P _{14} P _{16}- P _{15}^{2}+ P _{14} P _{15}}{ P _{13} P _{14}}\) is equal to\(......\)
- A \(15\)
- B \(14\)
- C \(13\)
- D \(16\)
Answer & Solution
Correct Answer
(D) \(16\)
Step-by-step Solution
Detailed explanation
\(Pn =\alpha^{ n }-\beta^{ n } \quad x ^{2}- x -4=0\) \(\frac{ P _{15} P _{16}- P _{14} P _{16}- P _{15}^{2}+ P _{14} P _{15}}{ P _{13} P _{14}}\) As \(P _{ n }- P _{ n -1}=\left(\alpha^{ a }-\beta^{ n }\right)-\left(\alpha^{ n -1}-\beta^{ n -1}\right)\)…
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