AP EAMCET · Maths · Quadratic Equation
If \((2 k-1) x^2-2(3 k-2) x+4 k>0\) for every \(x \in R\), then the sum of all possible integral values of \(k\) is
- A 21
- B 27
- C 36
- D 28
Answer & Solution
Correct Answer
(D) 28
Step-by-step Solution
Detailed explanation
For \( (2 k-1) x^2-2(3 k-2) x+4 k>0 \) for all \(x \in R\): \(2k-1 > 0 \implies k > \frac{1}{2}\) \(D \((-2(3k-2))^2 - 4(2k-1)(4k) \(4(3k-2)^2 - 16k(2k-1) \((9k^2-12k+4) - (8k^2-4k) \(k^2-8k+4 Roots of \(k^2-8k+4=0\) are \(k = \frac{8 \pm \sqrt{64-16}}{2} = 4 \pm 2\sqrt{3}\)…
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