Derive the quadratic formula (Hint: complete the square)
Firstly, the quadratic formula finds the roots of a quadratic equation.
So this means f(x) = 0. A general polynomial with highest power 2 looks like: ax2 + bx +c.
Usings the two facts we just stated, we solve for the roots of ax2 + bx +c = 0. ax2 + bx +c = 0
x2 + (b/a)x + (c/a) = 0
USINGING THE HINT
(x + (b/2a))2 - (b/2a)2 + (c/a) = 0
(x + (b/2a))2 = (b/2a)2 -(c/a)
Make the right hand side all one fraction
(x + (b/2a))2 = (b2/4a2) - (4ac/4a2)
(x + (b/2a))2 = (b2-4ac) / 4a2
Squareroot both sides
x + (b/2a) = (+/-) (b2-4ac)1/2 / 2a (The (+/-) comes from the squareroot having 2 sol's. e.g 41/2 = 2 or -2)
x = (-b (+/-) (b2-4ac)1/2) / 2a
RK
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