JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The sum of all integral values of \(\mathrm{k}(\mathrm{k} \neq 0\) ) for which the equation \(\frac{2}{x-1}-\frac{1}{x-2}=\frac{2}{k}\) in \(x\) has no real roots, is ..... .
- A \(95\)
- B \(76\)
- C \(66\)
- D \(70\)
Answer & Solution
Correct Answer
(C) \(66\)
Step-by-step Solution
Detailed explanation
\(\frac{2}{x-1}-\frac{1}{x-2}=\frac{2}{k}\) \(x \in R-\{1,2\}\) \(\Rightarrow k(2 x-4-x+1)=2\left(x^{2}-3 x+2\right)\) \(\Rightarrow k(x-3)=2\left(x^{2}-3 x+2\right)\) \(\text { for } x \neq 3, \quad \mathrm{k}=2\left(\mathrm{x}-3+\frac{2}{\mathrm{x}-3}+3\right)\)…
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