Question

If $\alpha ,\beta$ are the roots of the equation $2x^2+5x+6=0$, then find the equation whose roots are $\frac{1}{\alpha }and\frac{1}{\beta }$.

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

If $x_0$ is a root of the equation $2x^2+5x+6=0$ , we want to find the equation whose root is $\frac{1}{x_0}$

Let it be y.

$y=\frac{1}{x_0}or{x}_0=\frac{1}{y}$

To find the equation, whose roots are y, replace x by $\frac{1}{y}$(Because it satisfies the equation)

$\Rightarrow 2\times {\left(\frac{1}{y}\right)}^2+5\times \frac{1}{y}+6\Rightarrow 2+5y+6y^2=0\left(\text{Replace y by x}\right)\Rightarrow 6x^2+5x+2=0$

[change of variable does not affect the equation]

We can solve this by find the sum of the roots and product of the roots.