Suppose the roots of the equation 2x^2−5x−6=0 are α and β.find the quadratic equation with roots 1/α and 1/β.

The quadratic equation with roots 1/α and 1/β is

Solution:

Given, roots of equation

We have to find equation whose roots are 1/α, and 1/β.

We know that,

Now, we know that, general form of an equation is

Then, equation whose roots 1/α and 1/β is

from above given equation,