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