CBSE Class 10 Answered

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 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 take an integral value.