WBJEE · Maths · Application of Derivatives
Let \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) be three real numbers such that \(\mathrm{a}+2 \mathrm{~b}+4 \mathrm{c}=0\). Then the equation \(\mathrm{ax}^2+\mathrm{bx}+\mathrm{c}=0\)
- A has both the roots complex
- B hat its roots lying within \(-1 < x < 0\)
- C has one of roots equal to \(\frac{1}{2}\)
- D has its roots lying within \(2 < x < 6\)
Answer & Solution
Correct Answer
(C) has one of roots equal to \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
Hints: \(\frac{1}{4} \mathrm{a}+\frac{1}{2} \mathrm{~b}+\mathrm{c}=0\) \(\begin{aligned} & \left(\frac{1}{2}\right)^2 a+\left(\frac{1}{2}\right) b+c=0 \\ & \therefore x=\frac{1}{2} \end{aligned}\)
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