If ax2 - bx + 5 = 0 does not have two distinct real roots, find the minimum value of 5a + b.
2. Homework Equations
The Quadratic Formula
The Attempt at a Solution
Here, D = b2 - 4a(5) = b2 - 20a
D ≤ 0 ⇒ b2 ≤ 20a ⇒ b ≤ ±2√(5a)
Also, an obvious observation is that b ≤ 0, since, the quadratic does not have two distinct real roots, all coefficients and the constant are of same sign. So, for a, (-b), 5 to be all positive, b must be non-positive.
But how do I arrive at 5a + b?