Are There Only Three Ways to Solve Quadratic Equation?

1. Dec 4, 2014

bballwaterboy

In class, we've learned:

1.) Factoring and Setting Equal to Zero
2.) Completing the Square

Are there any other methods? Thanks.

2. Dec 4, 2014

mafagafo

A nice website.
Anyway, solving an equation (of any order or type) can be done in several different ways.
See that "Factoring and Setting Equal to Zero" does not solve anything. You do not set it to zero. Factoring here implies that one side will not have any terms.

You could also: graph it and see where it intercepts the x axis.
"Randomly" guess a root until you find one. (Remember to eat once in a while, otherwise you may perish during this task)

There are a few methods to numerically approximate a root.
$$\text{Let }p(x) = x^2 - 6x + 8. \text{ Find y such that }p(y) = 0.$$
Try 0. You get 8.
Try 3. You get -1.
From this you know that there is a possible value for y in the range (0, 3).

A computer or a calculator can do this rather quickly and with very good precision.

3. Dec 4, 2014

pasmith

(2) and (3) are the same method.

4. Dec 6, 2014

lurflurf

^you could say (1), (2), and (3) are the same method. It depends how you count them. You could also break each into several cases.
mafagafo has some good ideas numerical, graphical, and guessing based methods and many versions of each. Quadratic equations are simple, but trigonometry, differential equations, and linear algebra can be used to solve quadratics as well as higher polynomials.

5. Dec 7, 2014

Staff: Mentor

There is another way that sometimes works ask the teacher... :-)

6. Dec 9, 2014

bolbteppa

7. Dec 10, 2014

DivergentSpectrum

2 and 3 are the same, and as far as factoring goes, that only works if you already know one root

8. Dec 10, 2014

Staff: Mentor

It's not necessary to know one root in order to factor a quadratic polynomial.