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

Sum

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

#### Solution

Yes, consider the quadratic equation 2x2 + x – 4 = 0 with rational coefficient.

The roots ofthe given quadratic equation are

(-1 + sqrt(33))/4 and (-1 - sqrt(3))/4 are irrational.

Concept: Nature of Roots
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10