question

Asked by arindeep.singh | 26th 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.

Answered by Renu Varma | 28th Sep, 2020, 11:11: AM