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CBSE Class 10 Answered

question
Asked by arindeep.singh | 26 Sep, 2020, 10:41: AM
Expert Answer
Q: Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.
Solution:
Yes, there is a quadratic equation whose coefficients are rational but the roots are irrational
Here is an example:

The quadratic equation is x2 + 3x + 1 = 0

It has integral coefficients

Now D = b2 - 4ac = 32 - 4(1)(1) = 9 - 4 = 5

Here, sqrt{D} is not a perfect square. So, x can't be rational.

Hence, the roots are irrational.

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