Question 156
Let $a$ and $b$ be real numbers. Prove that the polynomial
$$
P(x) = x^{3} + (2a + 1)x^{2} + (2a^{2} + 2a - 3)x + b
$$
does not have three distinct rational roots.
$$
P(x) = x^{3} + (2a + 1)x^{2} + (2a^{2} + 2a - 3)x + b
$$
does not have three distinct rational roots.