Question

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

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

Answer 1

Answer: (A)

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