# Methods to Solve Quadratic Equations ?

• April 24th 2013, 11:02 AM
fanna1119
Methods to Solve Quadratic Equations ?
Hi,
So I was just wondering what are the different methods of solving Quadratic Equations.
And which one is the easiest or most useful to use ?
thanks (Wink)
• April 24th 2013, 11:21 AM
HallsofIvy
Re: Methods to Solve Quadratic Equations ?
1) Factor. If $ax^2+ bx+ c= (x- \alpha)(x- \beta)= 0$ then x= a and x= b are roots. One can theoretically always factor but there are just too many ways to try unless you restrict to integer coefficients. And not all quadratics can be factored with integer coefficients.

2) Complete the square. If $ax^2+ bx+ c= a(x- \alpha)^2+ \beta= 0$ then $x= \alpha\pm \frac{\sqrt{-beta/a}}{a}$.

3) Use the quadratic formula. Applying "complete the square" to the general $ax^2+ bx+ c= 0$ gives $x= \frac{-b\pm\sqrt{b^2- 4ac}}{2a}$.