JEE Mains · Maths · STD 11 - 8. sequence and series
Let the arithmetic mean of \(\frac{1}{a}\) and \(\frac{1}{b}\) be \(\frac{5}{16}\),\(a>2\). If \(\alpha\) is such that \(a, 4, \alpha, b\) are in A.P., then the equation \(\alpha x^2-a x+2(\alpha-2 b)=0\) has :
- A One root in (1, 4) and another in (-2, 0)
- B One root in (0, 2) and another in (-4, -2)
- C Complex roots of magnitude less than 2
- D Both roots in the interval (-2, 0)
Answer & Solution
Correct Answer
(A) One root in (1, 4) and another in (-2, 0)
Step-by-step Solution
Detailed explanation
\(a=4-d, \alpha=4+d, b=4+2d\) \(\Rightarrow(4+d)x^{2}-(4-d)x+2(4+d-8-4d)=0\) \(\Rightarrow(4+d)x^{2}-(4-d)x+2(-4-3d)=0\) Also \(\frac{\frac{1}{a}+\frac{1}{b}}{2}=\frac{5}{16}\) \(\Rightarrow \frac{\frac{1}{4-d}+\frac{1}{4+2 d}}{2}=\frac{5}{16}\) \(\Rightarrow d =2\) Equation…
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