The theory of equations!

Algebra Level 4

Let $a, b, c,$ and $d$ be four positive integers such that $ad$ is odd and $bc$ is even. For the equation below, what can be said of its roots? $\large ax^{3} +bx^{2}+cx+d=0$

At least one irrational root All three rational roots All three integral roots Nothing can be said surely