Question

Does a quadratic equation with integral coefficient has always integral roots. Justify you
answer.​

Answer 1

A quadratic equation with integral coefficients does not always have integral roots

The equation:

$6x ^{2} - 5x + 1 = 0$

roots are 1/2 and 1/3

Sum of roots 1/2+1/3=3+2/6=5/6

product of roots =1/6

here coefficients are integers but roots are non integral and rational