Question 1

Algebra Level 3

Let $f(x), g(x), h(x)$ be quadratic polynomials having positive leading coefficient, each one having real and distinct zeros. If each pair of $f(x), g(x)$ and $h(x)$ has a common linear factor of $x$ , then the roots of the equation $f(x) + 2g(x) + 3h(x) = 0$ :

may be real and distinct may be conjugate imaginary are always conjugate imaginary may be real and equal