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.
$\displaystyle ax^2 + bx + c $
$\displaystyle a\left( x^2 + \frac{b}{a} \cdot x + \frac{c}{a} \right) $
r,s are roots of the equation so we can write the equation like this
$\displaystyle (x-r)(x-s)= x^2 + \frac{b}{a} \cdot x + \frac{c}{a} $
$\displaystyle x^2 +x(-r-s) + rs = x^2 + \frac{b}{a} \cdot x + \frac{c}{a}$
$\displaystyle -r-s = \frac{b}{a} \Rightarrow r+s = \frac{-b}{a} $
$\displaystyle rs = \frac{c}{a} $