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JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The least integral value \(\alpha \) of \(x\) such that \(\frac{{x - 5}}{{{x^2} + 5x - 14}} > 0\) , satisfies
- A \({\alpha ^2} + 3\alpha - 4 = 0\)
- B \({\alpha ^2} - 5\alpha + 4 = 0\)
- C \({\alpha ^2} - 7\alpha + 6 = 0\)
- D \({\alpha ^2} + 5\alpha - 6 = 0\)
Answer & Solution
Correct Answer
(A) \({\alpha ^2} + 3\alpha - 4 = 0\)
Step-by-step Solution
Detailed explanation
\(\frac{x-5}{x^{2}+5 x-14}>0\) \(\Rightarrow {x^2} + 5x - 14 < x - 5\) \(\Rightarrow x^{2}+4 x-9<0\) \(\Rightarrow \alpha=-5,-4,-3,-2,-1,0,1\) \(\alpha=-5\) does not satisfy any of the options \(\alpha=-4\) satisfy the option \((a) \alpha^{2}+3 \alpha-4=0\)
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