Question

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

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

Answer 1

Answer: (C)

$\frac{37 }{ 6}$

Answer 2

Given equation is
$a x^{2}-b x+a=0 \,.....(i)$
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 E (ii), we get
$6+\frac{1}{6}=\frac{b}{a} \Rightarrow \frac{b}{a}=\frac{37}{6}$