Let $m$ be a real number. If the quadratic equation $x^2+mx+4 = 2x^2 + 17x + 8$ has two distinct real roots, then what are the possible values of $m$? Express your answer in interval notation.
x^2 + mx + 4 = 2x^2 + 17x + 8 rearrange as
x^2 + (17 - m)x + 4 = 0
If we have two distinct roots, the discriminant > 0 ...... so....
(17 - m)^2 - 4(1)(4) > 0
(17 - m)^2 > 16 take the positive root
17 - m > 4
13 > m
m < 13
+1756 
