Question

If $\alpha$ and $\beta$ are the roots of equation $a{x}^2+bx+c=0$, then the roots of equation $c{x}^2+bx+a=0$ are

• A. $\frac{1}{\alpha },\frac{1}{\beta }$
• B. $-\frac{1}{\alpha },-\frac{1}{\beta }$
• C. $\frac{1}{\alpha },-\frac{1}{\beta }$
• D. $-\frac{1}{\alpha },\frac{1}{\beta }$

Answer 1

The correct option is A $\frac{1}{\alpha },\frac{1}{\beta }$

As $\alpha ,\beta$ are roots of ${ax}^2+bx+c=0$

Replacing $x\to \frac{1}{x}$, we get

$a{\left(\frac{1}{x}\right)}^2+b\left(\frac{1}{x}\right)+c=0$

$\Rightarrow {cx}^2+bx+c=0$

Hence, roots are $\frac{1}{\alpha },\frac{1}{\beta }$.