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

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Sum

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

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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
  Is there an error in this question or solution?

APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 4 Quadatric Euation
Exercise 4.2 | Q 4 | Page 39
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