CBSE Class 10 Answered

question

Asked by arindeep.singh | 26 Sep, 2020, 10:39: AM

Expert Answer

Q: Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?

Solution:

Yes, it is possible that a quadratic equation with distinct irrational coefficients have rational roots.

It is because, the roots are rational if the discriminant is a perfect square. So, it depends upon the discriminant and not on the coefficients.

Here is an example:

square root of 3 straight x squared minus square root of 27 straight x plus square root of 12 equals 0 straight x equals fraction numerator negative straight b plus-or-minus square root of straight b squared minus 4 ac end root over denominator 2 straight a end fraction equals fraction numerator square root of 27 plus-or-minus square root of 27 minus 4 open parentheses square root of 3 close parentheses open parentheses square root of 12 close parentheses end root over denominator 2 square root of 3 end fraction equals fraction numerator 3 square root of 3 plus-or-minus square root of 27 minus 24 end root over denominator 2 square root of 3 end fraction equals fraction numerator square root of 3 open parentheses 3 plus-or-minus 1 close parentheses over denominator 2 square root of 3 end fraction equals fraction numerator 3 plus-or-minus 1 over denominator 2 end fraction equals 2 space or space 1

Answered by Renu Varma | 28 Sep, 2020, 11:00: AM

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