JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The numbers of pairs \((a, b)\) of real numbers, such that whenever \(\alpha\) is a root of the equation \(x^{2}+a x+b=0, \alpha^{2}-2\) is also a root of this equation, is :
- A \(6\)
- B \(2\)
- C \(4\)
- D \(8\)
Answer & Solution
Correct Answer
(A) \(6\)
Step-by-step Solution
Detailed explanation
Consider the equation \(x^{2}+a x+b=0\) If has two roots (not necessarily real \(\alpha \, \& \beta\) ) Either \(\alpha=\beta\) or \(\alpha \neq \beta\) Case \((1)\) If \(\alpha=\beta\), then it is repeated root. Given that \(\alpha^{2}-2\) is also a root So,…
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