Question 31
Let $P(x) = a x^3 + (b - a) x^2 - (c + b) x + c$, $Q(x) = x^4 + (b - 1) x^3 + (a - b) x^2 - (c + a) x + c$ be polynomials of the indeterminate $x$, where $a, b, c$ are nonzero real numbers and $b \gt 0$. If the polynomial $P(x)$ has three different real roots $x_0, x_1, x_2$, which are also roots of the polynomial $Q(x)$, then:
(a) Prove that: $abc \gt 28$.
(b) If $a, b, c$ are nonzero integers with $b \gt 0$, find their possible values.
(a) Prove that: $abc \gt 28$.
(b) If $a, b, c$ are nonzero integers with $b \gt 0$, find their possible values.