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
1) Factor. If $\displaystyle ax^2+ bx+ c= (x- \alpha)(x- \beta)= 0$ 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 $\displaystyle ax^2+ bx+ c= a(x- \alpha)^2+ \beta= 0$ then $\displaystyle x= \alpha\pm \frac{\sqrt{-beta/a}}{a}$.
3) Use the quadratic formula. Applying "complete the square" to the general $\displaystyle ax^2+ bx+ c= 0$ gives $\displaystyle x= \frac{-b\pm\sqrt{b^2- 4ac}}{2a}$.