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question Asked by arindeep.singh | 26 Sep, 2020, 10:35: AM Expert Answer
Q: A quadratic equation with integral coefficient has integral roots. Justify you answer.
Solution:

It is not neccesary that a quadratic equation with integral coefficients has integral roots because it will depend on the discriminant, whether it is a perfect square or not and along with that (-b+D^(1/2))&(-b-D^(1/2)) should be a multiple of 2a.

Let us take an example to disprove this statement

Ex:

Quadratic equation is x+ 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 take an integral value.

t is not neccesary because a quadratic with integral coefficient has an integral root or not will depend on discriminant , whether it is a perfect square or not and along with that (-b+D^(1/2))&(-b-D^(1/2)) should be a multiple of 2a.

Ex: equation X^2+3X+1=0 has integral coefficient but not integral roots.
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