SOLUTION: Show, that if p and q are two solutions of a quadratic equation ax^2 + bx + c = 0 (a cannot equal zero) then p + q = -b/a and p * q = c/a I would really appreciate help with thi

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Show, that if p and q are two solutions of a quadratic equation ax^2 + bx + c = 0 (a cannot equal zero) then p + q = -b/a and p * q = c/a I would really appreciate help with thi      Log On


   

Question 1122552: Show, that if p and q are two solutions of a quadratic equation ax^2 + bx + c = 0 (a cannot equal zero) then p + q = -b/a and p * q = c/a
I would really appreciate help with this problem!

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
use the quadratic formula for roots, then
:
p = (-b +sqrt(b^2 -4ac))/2a
:
q = (-b -sqrt(b^2 -4ac))/2a
:
p+q = ((-b +sqrt(b^2 -4ac) +(-b -sqrt(b^2 -4ac)))/2a =
:
-2b/2a =
:
-b/a
:
p*q = (-b +sqrt(b^2 -4ac))/2a * (-b -sqrt(b^2 -4ac))/2a =
:
(b^2 -b^2 +4ac)/4a^2 =
:
4ac/4a^2 =
:
c/a
: