Question

If one of the roots of the quadratic equation $a{x}^2-bx+a=0$ is $6$, then value of $\frac{b}{a}$ is equal to

• A. $\frac{1}{6}$
• B. $\frac{11}{6}$
• C. $\frac{37}{6}$
• D. $\frac{6}{11}$
• E. $\frac{6}{37}$

Answer 1

Answer: (C)

Given equation is
$a{x}^2-bx+a=0.....(i)$
and one root is 6 .
Let $\alpha$ and $\beta$ are the roots of the equation and $\alpha =6$. From the equation
$\alpha +\beta =\frac{b}{a}$
$\Rightarrow 6+\beta =\frac{b}{a}.....(ii)$
and $\alpha \beta =\frac{a}{a}=1\Rightarrow \beta =\frac{1}{\alpha }=\frac{1}{6}$
By putting $\beta =\frac{1}{6}$ in Eq. (ii), we get
$6+\frac{1}{6}=\frac{b}{a}\Rightarrow \frac{b}{a}=\frac{37}{6}$