JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The set of all values of \(\mathrm{k}\,>\,-1\), for which the equation \(\left(3 x^{2}+4 x+3\right)^{2}-(k+1)\left(3 x^{2}+4 x+3\right)\) \(\left(3 x^{2}+4 x+2\right)+k\left(3 x^{2}+4 x+2\right)^{2}=0\) has real roots is:
- A \(\left(1, \frac{5}{2}\right]\)
- B \([2,3)\)
- C \(\left[-\frac{1}{2}, 1\right)\)
- D \(\left(\frac{1}{2}, \frac{3}{2}\right]-\{1\}\)
Answer & Solution
Correct Answer
(A) \(\left(1, \frac{5}{2}\right]\)
Step-by-step Solution
Detailed explanation
\(\left(3 x^{2}+4 x+3\right)^{2}-(k+1)\left(3 x^{2}+4 x+3\right)\left(3 x^{2}+4 x+2\right)+\mathrm{k}\left(3 \mathrm{x}^{2}+4 \mathrm{x}+2\right)^{2}=0\) Let \(3 x^{2}+4 x+3=a\) and \(3 x^{2}+4 x+2=b \Rightarrow b=a-1\) Given equation becomes…
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