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Question: Answered & Verified by Expert
If 2 and 6 are the roots of the equation $a x^2+b x+1=0$, then the quadratic equation, whose roots are $\frac{1}{2 a+b}$ and $\frac{1}{6 a+b}$, is :
MathematicsQuadratic EquationJEE MainJEE Main 2024 (04 Apr Shift 1)
Options:
  • A $2 x^2+11 x+12=0$
  • B $x^2+8 x+12=0$
  • C $4 x^2+14 x+12=0$
  • D $x^2+10 x+16=0$
Solution:
1695 Upvotes Verified Answer
The correct answer is: $x^2+8 x+12=0$
$\begin{aligned} & \text { Sum }=8=-\frac{b}{a} \\ & \text { Product }=12=\frac{1}{a} \quad \Rightarrow a=\frac{1}{12} \\ & b=-\frac{2}{3} \\ & 2 a+b=\frac{2}{12}-\frac{2}{3}=-\frac{1}{2} \\ & 6 a+b=\frac{6}{12}-\frac{2}{3}=-\frac{1}{6} \\ & \text { sum }=-8 \\ & P=12 \\ & x^2+8 x+12=0\end{aligned}$

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