Question 24
Let $f(x) = x^{2} + (2a - 1)x - a - 3$, where $a$ is a real parameter.
a) Prove that the equation $f(x) = 0$ has two distinct real roots $x_{1}$ and $x_{2}$.
b) Find all values of $a$ such that $x_{1}^{3} + x_{2}^{3} = -72$.
a) Prove that the equation $f(x) = 0$ has two distinct real roots $x_{1}$ and $x_{2}$.
b) Find all values of $a$ such that $x_{1}^{3} + x_{2}^{3} = -72$.