Question

How many methods are there for solving quadratic equations? And which is a preferred method?

Answer 1

There are Four different methods of solving a quadratic equation;

1)Factoring

2)The square root property

3)Completing the square

4)The quadratic formula.

Factoring is a somewhat difficult method when it comes to quadratic equations, since you have to find all factors of the coefficients and see if they work. It does work on problems such as x^2 + 19x + 84 = 0, since 84 = 12*7 and 12+7 = 19. However, in some instances, factoring might already "assume" you know the zeros of the quadratic.

The square root property only applies to x^2 = c --> x = +/- sqrt(c). For example, if the quadratic is x^2 = 9, then x = 3 or -3.

You can complete the square anytime, as long as you are good with arithmetic. The quadratic equation x^2 + 8x + 3 = 0 can be turned into a square by adding 13 to both sides, i.e. x^2 + 8x + 16 = 13 --> (x+4)^2 = 13, then take the +/- square root of both sides.

The quadratic formula always works for a quadratic. Use this if the other methods fail, or if you do not wish to factor or complete the square.

Therefore quadratic formula is preferred for solving any type of quadratic equations.