All the roots of
x^2 + px + q = 0 are real, where p and q are real numbers. Prove that all the roots of
x^2 + px + q + (x + a)(2x + p) = 0 are real, for any real number a.
Since x^2 + px + q has real roots and (x + a)(2x + p) has real roots, x^2 + px + q + (x + a)(2x + p) also has real roots.
