ax^2 + bx + x = 0. Solutions: r,s
I think you mean
ax^2 + bx + c = 0.
Let
And
Hence
Hence and
2nd part should fall into place now
Suppose a, b, and c are fixed real numbers such that
b^2 - 4ac ≥ 0. Let r and s be the solutions of
ax^2 + bx + x = 0.
(a) Use the quadratic formula to show that r + s = -b/a and
rs = c/a.
(b) Use part (a) to verify that ax^2 + bx + c =
a(x - r)(x - s).