Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?

To do:

We have to find whether there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals.

Solution:

It is not necessary that a quadratic equation with irrational coefficients has irrational roots.

For example,

The roots of the quadratic equation $\sqrt3x^2-7\sqrt3x+12\sqrt3=0$ are $3$ and $4$.

Here, 3 and 4 are rational whereas the coefficients of the quadratic equation are irrational.

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Updated on: 10-Oct-2022

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