Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$Since,\frac{\alpha }{\beta }=\frac{m}{n}\Rightarrow \frac{\alpha +\beta }{\alpha -\beta }=\frac{m+n}{m-n}\Rightarrow \frac{(\alpha +\beta {)}^2}{(\alpha +\beta {)}^2-4\alpha \beta }=\frac{(m+n{)}^2}{(m+n{)}^2-4mn}\Rightarrow \frac{4\alpha \beta }{(\alpha +\beta {)}^2}=\frac{4mn}{(m+n{)}^2}\Rightarrow \frac{c/a}{b^2/a^2}=\frac{mn}{(m+n{)}^2}\Rightarrow ac(m+n{)}^2=mn{b}^2$