Question

If $a,b,c$ are in $AP$ and one root of the equation $a{x}^2+bx+c=0$ is $2$, then the other root is

• A. $\frac{3}{4}$
• B. $\frac{-3}{4}$
• C. $-\frac{5}{4}$
• D. $\frac{-5}{2}$

Answer 1

The correct option is C $-\frac{5}{4}$

Given $a,b,c$ are in A.P
$a+c=2b$ ....(1)
Given equation is $a{x}^2+bx+c=0$
Given $\alpha =2$
Let the other root be $\beta$
$2+\beta =-\frac{b}{a}$ and $2\beta =\frac{c}{a}$
$\Rightarrow 2+\beta =-\frac{c+a}{2a}$
$\Rightarrow 2+\beta =-\frac{1}{2}\frac{c}{a}-\frac{1}{2}$
$\Rightarrow 2+\beta =-\beta -\frac{1}{2}$
$\Rightarrow \beta =-\frac{5}{4}$