Question

If $\alpha ,\beta$ are the roots of $a{x}^2+c=bx$, then the equation $(a+cy{)}^2=b^{2}y$ in y has the roots

• A.
• B.
  
• C.
• D.

Answer 1

The correct option is D

$a{x}^2-bx+c=0$ $\Rightarrow \alpha +\beta =\frac{b}{a}and\alpha \beta =\frac{c}{a}$ $Clearly,y=\frac{1}{x^2}$ $\Rightarrow a.\frac{1}{y}-\frac{b}{\sqrt{y}}+c=0$ $ora-b\sqrt{y}+cy=0$ $or{b}^{2}y=(a+cy{)}^2$ $\Rightarrow (a+cy{)}^2=b^{2}yhasroots\frac{1}{{\alpha }^2},\frac{1}{{\beta }^2}$