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

Sum

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

#### Solution

Yes, consider the quadratic equation with all distinct irrationals coefficients

i.e., sqrt(3)x^2 - 7sqrt(3)x + 12sqrt(3) = 0.

The roots of this quadratic equation are 3 and 4

Which are rationals.

Concept: Nature of Roots
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10