Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.

To do:

We have to find whether there exist a quadratic equation whose coefficients are rational but both of its roots are irrational.

Solution:

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

For example,

The roots of the quadratic equation $x^2+x-5=0$ are $\frac{-1-\sqrt{21}}{2}$ and $\frac{1+\sqrt{21}}{2}$.

Here, $\frac{-1-\sqrt{21}}{2}$ and $\frac{1+\sqrt{21}}{2}$ are not rational.

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Updated on: 10-Oct-2022

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