WBJEE · Maths · Quadratic Equation
If \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(a x^{2}+b x+c=0\) and \(3 b^{2}=16 a c\) then
- A \(\alpha=4 \beta\) or \(\beta=4 \alpha\)
- B \(\alpha=-4 \beta\) or \(\beta=-4 \alpha\)
- C \(\alpha=3 \beta\) or \(\beta=3 \alpha\)
- D \(\alpha=-3 \beta\) or \(\beta=-3 \alpha\)
Answer & Solution
Correct Answer
(C) \(\alpha=3 \beta\) or \(\beta=3 \alpha\)
Step-by-step Solution
Detailed explanation
Given that, \((\alpha, \beta)\) are roots of the quadratic equation and \(\begin{aligned} a x^{2}+b x+c &=0 \\ 3 b^{2} &=16 a c \end{aligned}\) \(\therefore\) \(\alpha+\beta=\frac{-b}{a}\) and \(\alpha \beta=\frac{c}{a}\) From Eq. (i), we get…
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