How to Find the Zeros of a Function

Step-by-Step Guide

1. 1

   Step 1: Set up your equation so that it looks something like x2 + 5x + 4.

   Start with your biggest terms and move successively down, until you get to your constant.
   
   You want your big polynomial, such as or x2, to be the first term, and then to successively go down to smaller terms, until the last term is just a single number, like 8 or
   4.
   
   Add an equals sign and a zero to the end of each term.
   
   Polynomial terms that have been ordered correctly: x2 + 5x + 6 = 0 x2
   - 2x – 3 = 0 Polynomial terms that have been ordered incorrectly: 5x + 6 =
   -x2 x2 = 2x + 3
2. 2

   Step 2: Give your equation an "a"

   There's no math involved in this step.
   
   It's purely for setting things up so that you can factor easier when the time comes.
   
   Think of your equation as having a format.
   
   The format of the equation is ax2 ± bx ± c =
   0.
   
   Simply find out the a, b, and c values in your equation.
   
   Here are some examples: x2 + 5x + 6 = 0 a = 1 (no number in front of "x" = 1, as there is still one "x" being squared) b = 5 c = 6 x2
   - 2x – 3 = 0 a = 1 (no number in front of "x" = 1, as there is still one "x" being squared) b =
   -2 c =
   -3 , A factor pair is two numbers that, multiplied together, equal that number.
   
   Pay special attention to negative numbers.
   
   Two negative numbers multiplied together equal a positive number.
   
   Order doesn't matter here. ("1 x 4" is the same as "4 x 1".) Equation: x2 + 5x + 6 = 0 Factor pairs of 6, or c: 1 x 6 = 6
   -1 x
   -6 = 6 2 x 3 = 6
   -2 x
   -3 = 6 , Look at your b value and find which of your factor pairs add up to that number. b value = 5 Factor pair whose sum equals 5 = 2 and 3 2 + 3 = 5 , A binomial is just (x ± number)(x ± number).
   
   How do you know if it's a plus sign or minus sign that you put into the binomial? You look at the factor pair numbers: positive number = plus sign, negative number = minus sign.
   
   Here is the factor pair that we've put into a binomial: (x + 2)(x + 3) = 0 , Break the two binomials apart — (x + 2) = 0 and (x + 3) = 0 — and then "solve" the equation by adding or subtracting to isolate the variable and the constant: (x + 2) = 0 becomes x =
   -2 (x + 3) = 0 becomes x =
   -3 , These are the zeroes of your function.
3. 3

   Step 3: and "c" number.

4. 4

   Step 4: Write down all the factor pairs of your "c" value.

5. 5

   Step 5: Find the factor pair that

6. 6

   Step 6: when added together

7. 7

   Step 7: equals "b".

8. 8

   Step 8: Put that factor pair into two binomials.

9. 9

   Step 9: Solve each factor by moving the constant over to the other side of the equation.

10. 10

    Step 10: Finished.

Detailed Guide

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