Question 20.

$f(x) \ge 0$ for all real numbers $x$, so $D \le 0$

Since $f(2) = 0$ therefore $x = 2$ is a root of $f(x)$

Since the discriminant of $f(x)$ is less than equal to 0 and 2 is a root so we can conclude that $D = 0$

Therefore $f(x) = a(x - 2)^2$

$f(4) = 6$

or, $6 = a(x - 2)^2$

$a = \frac{3}{2}$