Question

If one root of the equation $a{x}^2$+px + q = 0 be n times the other root, then

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Let the roots are $\alpha$ and $n\alpha$

Sum of roots, $\alpha andn\alpha =-\frac{b}{a}\Rightarrow \alpha =-\frac{b}{a(n+1)}$ ........(i)

and product, $\alpha .n\alpha =\frac{c}{a}\Rightarrow {\alpha }^2=\frac{c}{na}$ .......(ii)

From (i) and (ii), we get

$\Rightarrow {[-\frac{b}{a(n+1)}]}^2=\frac{c}{na}\Rightarrow \frac{b^2}{a^2(n+1{)}^2}=\frac{c}{na}$

$\Rightarrow n{b}^2=ac(n+1{)}^2$