When given the quadratic equation with integer roots: mx^2 - (m-2)x + m - 8 = 0
What's the value of integer parameter m? And what are the integer roots?
The discriminant of this quadratic is
\(b^2 - 4ac = (-m+2)^2 - 4(m)(m-8) = -3m^2 + 28m + 4\)
For starters, the discriminant has to be nonnegative, which limits our values of m to the solutions of -3m^2 + 28m + 4 >= 0. So, m can be 0, 1, 2, 3, or 4. From there, it's easy to try each individual value until you find an equation with integer roots.