The Quadratic Formula

The Quadratic Formula

The solutions of ax + bx + c = 0 are given by

 

x = \frac{-b\mp \sqrt{b^{2}-4ac}}{2a}

 

The formula also holds when a < 0. A similar proof would show this, but we will not consider it here.

 

To solve a quadratic equation:

a. Check for the form x2 = d  or (x + c)2 = d.

 

b. If it is not in the form of step (a), write it in standard form

ax2 + bx + c = 0  with a and b nonzero.

 

c. Then try factoring.

 

d. If it is not possible to factor or if factoring seems difficult, use the

quadratic formula.

 

The solutions of a quadratic equation cannot always be found by

factoring. They can always be found using the quadratic formula.

 

 

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