Question

If one of the roots of equation $x^2+ax+3=0$ is $3$ and one of the roots of the equation $x^2+ax+b=0$ is three times the other root, then the value of $b$ is

• A. $3$
• B. $4$
• C. $2$
• D. $1$

Answer 1

The correct option is A $3$

Let $\alpha$ and $3$ are the roots of the equation $x^2+ax+3=0$

$⟹(x-3)(x-\alpha )=x^2+ax+3$

$⟹x^2-(\alpha +3)x+3\alpha =x^2+ax+3$

Equating the coefficients, we get
$3\alpha =3\Rightarrow \alpha =1$

and $3+\alpha =-a\Rightarrow a=-4$

Again, let $\beta$ and $3\beta$ are the roots of the equation $x^2+ax+b=0$.

$⟹(x-\beta )(x-3\beta )=x^2+ax+b$

$⟹x^2-(\beta +3\beta )x+{\beta }^2=x^2+ax+b$

$\therefore \beta +3\beta =-a\Rightarrow 4\beta =4$ ...... $[\because a=-4]$

$\Rightarrow \beta =1$

and $\beta \times 3\beta =b\Rightarrow 3\times 1=b\Rightarrow b=3$