Question

The factors of quadratic equation are rational for what value of

Answer 1

let the quadratic equation be

$a {x}^{2} + bx + c = 0$

for rational factors

a≠0 and d ≥ 0

Answer 2

suppose a quadratic equation as,

$a {x}^{2} + bx + c$

if all a, b, c are rational and the Discriminant(D) is a perfect square then the roots of the equation will always be rational.

in other words if,

${b}^{2} - 4(a)(c) = {t}^{2}$

where t is a rational number then the roots of the equation will always be rational.