Question

How do you find the discriminant and how many solutions does `m^2-8m=-14` have?

Answer 1

First, add 14 to both sides to get `m^2-8m+14=0`.

This is in standard form like `am^2+bm+c = 0`, with `a=1`, `b=-8` and `c=14`.

The discriminant is `b^2-4ac = (-8)^2-4*1*14 = 64 - 56 = 8`.

Since this is positive, the quadratic has 2 distinct real solutions.

Note that since the discriminant is not a square number, the solutions are not rational, let alone integers.