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```					                      Quadratic Formula Examples

A Quadratic equation is a univariate polynomial equation of the second degree. A general quadratic
equation can be written in the form

Ax2 + bx + c = 0

When you're solving quadratics in your homework, you can often get a "hint" as to the "best" method to
use, based on the topic and title of the section. For instance, if you're working on the homework in the
"Solving by Factoring" section, then you know that you're supposed to solve by factoring. But in the
chapter review and on the test, you don't know which section the quadratic came from. Which method
should you use? You could use the Quadratic Formula for everything, but the Formula can be
"overkill". For example:

Solve (x + 1)(x – 3) = 0.

This is a quadratic, and I'm supposed to solve it. I could multiply the left-hand side, simplify to find the
coefficients, plug them into the Quadratic Formula, and chug away to the answer.

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But why would I? I mean, for heaven's sake, this is factorable, and they've already factored it and set it
equal to zero for me. While the Quadratic Formula would give me the correct answer, why bother with
it? Instead, I'll just solve the factors:

(x + 1)(x – 3) = 0
x + 1 = 0 or x – 3 = 0
x = –1 or x = 3
The solution is x = –1, 3

Solve x2 + x – 4 = 0.
This one doesn't factor (since there are no factors of (1)(–4) = –4 that add to +1), and this isn't
formatted as "(squared part) equals (a number)", so I can't use square-rooting to solve. This leaves me
with completing the square (yuck!) or the Quadratic Formula. I'll use the Formula: The solution is

Solve x2 – 3x – 4 = 0.
x2 – 3x – 4 = 0
(x + 1)(x – 4) = 0
x + 1 = 0 or x – 4 = 0
x = –1 or x = 4
The solution is x = –1, 4

Solve x2 – 4 = 0.
This quadratic has just two terms, and nothing factors out of both, so it's a difference of squares (so I
can factor) or it can be reformatted as "(squared part) equals (a number)" so I can square-root both
sides. In this case, I can factor:
x2 – 4 = 0
(x + 2)(x – 2) = 0
x + 2 = 0 or x – 2 = 0
x = –2 or x = 2
The solution is x = ± 2

Math.Edurite.com                                                            Page : 2/3
Thank You

Math.Edurite.Com

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