JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The number of integral values of \(m\) for which the quadratic expression, \((1 + 2m)x^2 -2(1+ 3m)x + 4(1 + m),\) \(x\in R,\) is always positive, is
- A \(3\)
- B \(8\)
- C \(7\)
- D \(6\)
Answer & Solution
Correct Answer
(C) \(7\)
Step-by-step Solution
Detailed explanation
Expression is always positive it \(2 \mathrm{m}+1>0 \Rightarrow \mathrm{m}>-\frac{1}{2}\) and \(D<0 \Rightarrow m^{2}-6 m-3<0\) \(3 - \sqrt {12} < m < 3 + \sqrt {12} ..........(iii)\) \(\therefore\) Common interval is \(3-\sqrt{12}<\mathrm{m}<3+\sqrt{12}\) \(\therefore \)…
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