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. $\left(m n c\right)^{2}=ab \, \left(m + n\right)^{2}$

Answer 1

Answer: (A)

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