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Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?
We have to find whether there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals.
It is not necessary that a quadratic equation with irrational coefficients has irrational roots.
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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