Question

If the roots of the equation $a{x}^2+bx+c=0$ are in the ratio $m:n$ , then

• A. $mn{b}^2=ac{\left(m+n\right)}^2$
• B. $b^2\left(m+n\right)=mn$
• C. $m+n=b^{2}mn$
• D. ${\left(mnc\right)}^2=ab{\left(m+n\right)}^2$

Answer 1

Answer: (A)

Let the roots are $mr$ and $nr$
$mr+nr=\frac{-b}{a}\Rightarrow r\left(m+n\right)=\frac{-b}{a}\dots \left(1\right)$
and $mn{r}^2=\frac{c}{a}\dots \left(2\right)$
Eliminating $r$ , we get
$b^{2}mn=ca{\left(m+n\right)}^2$