Question

One root of the quadratic equation x^2 − 2x + m = 0 is 9. If the other root is n, what is n−m?

Answer 1

$9^2-2*9+m=0\\ \\ 81-18+m=0\\ \\ m=-63$

$x^{2} -2x-63=0\\ \\ \Delta=(-2)^2-4.1.(-63)=4+252=256\\ \\ x=\frac{2 \pm 16}{2}\\ \\ x_1=\frac{18}{2}=9\\ \\ n=x_2=\frac{-14}{2}=-7\\ \\ n-n=-7-(-63)=-7+63=56$