TS EAMCET · Maths · Quadratic Equation
If the equation \(x^2-3 a x+a^2-2 a-\mathrm{K}=0\) has different real roots for every rational number \(a\), then K lies in the interval
- A \(0 < K < \frac{4}{5}\)
- B \(-\infty < \mathrm{K} < \frac{4}{5}\)
- C \(\frac{4}{5} < K < \infty\)
- D \(-\infty < K < \infty\)
Answer & Solution
Correct Answer
(C) \(\frac{4}{5} < K < \infty\)
Step-by-step Solution
Detailed explanation
\(D = (-3a)^2 - 4(1)(a^2-2a-K) > 0\) \(9a^2 - 4a^2 + 8a + 4K > 0\) \(5a^2 + 8a + 4K > 0\) For \(5a^2 + 8a + 4K > 0\) to hold for all \(a\), its discriminant must be less than 0. \(D_a = 8^2 - 4(5)(4K) \(64 - 80K \(64 \(K > \frac{64}{80}\)…
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