examday

/TMUA

Let $P_1(x)$, $P_2(x)$ and $P_3(x)$ be three quadratic polynomials with real coefficients. The polynomial $Q(x)=P_1(x)P_2(x)P_3(x)$ has exactly $5$ distinct real roots.

Let $\Delta_i$ be the discriminant of $P_i(x)$ for $i=1,2,3$. Which of the following statements must be true?