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## Homework Statement

If ax

^{2}- bx + 5 = 0

**does not**have two distinct real roots, find the minimum value of 5a + b.

2. Homework Equations

2. Homework Equations

The Quadratic Formula

## The Attempt at a Solution

Here, D = b

^{2}- 4a(5) = b

^{2}- 20a

D ≤ 0

**⇒**b

^{2}≤ 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?

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