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JEE Main 20244 AprilMorning Shift

Exam: JEE Main
Year: 2024
Date: 4 April
Shift: Morning Shift
Subject: Mathematics
Chapter: Quadratic Equation

JEE Main 2024 · 4 April · Morning Shift · Mathematics · Quadratic Equation

If 2 and 6 are the roots of the equation a x^2+b x+1=0 , then the...

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 :

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 $x^2+10 x+16=0$

Correct answer

B. $x^2+8 x+12=0$

Step-by-step solution

\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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