In this problem we find all k such that x2−6x+k>17 for all values of x.
(1) If a quadratic in x is greater than zero for all values of x, then can it have real roots?
(2) How can you tell whether or not a quadratic has real roots?
(3) Use your answers to (a) and (b) to find all values of k such that x2−6x+k>17 for all values of x.