Question

please help solve this F(x)= x2 -5x-36

Answer 1

solve what? this is a function. what do you want to do with it?

Answer 2

zero of the polynomial function

Answer 3

is the first term x^2?

Answer 4

yes

Answer 5

ok, so you want to know what numbers multiply to get -36 but add to get -5

Answer 6

ok (x-9) and (X+4)

Answer 7

so options for -36 = (-1, 36), (-2,18), (-3,12), (-6,6), (-9,4), (-12,3)... so on

Answer 8

exactly!

Answer 9

thats as far as I got

Answer 10

so (x-9) * (x+4) distributes to get the right side of the equation

Answer 11

so what values could x have to make the factored version multiple to zero? it's whatever makes the individual factored terms "0" - since anything multiplied by zero is 0

Answer 12

so the first one is (x-9) = 0 OR (x+4) = 0 - those are the roots, solve for x in each case

Answer 13

in the first case, x=9, since (9-9)=0, and 0*(x+4) = 0. So 9 is one root

Answer 14

what is the other one? it's the number that makes (x+4) = 0

Answer 15

so you can do that =)

Answer 16

-4

Answer 17

x=-4

Answer 18

exactly, so you have your two roots =). 9 and -4

Answer 19

So the entire thought process is:
1. F(x)= x^2 -5x-36 - find the roots - ok so that means what values of x makes F(X)=0

2. Oh crap, that's hard to just guess and check. I better factor it.

3. F(x) = (x-9)*(x+4) //factored and equivalent

4. OK, so now it's easy to see. The function will equal zero when either (X-9) =0 , OR (x+4) =0.

5. x=9, or x=-4

Answer 20

ok, so is that the answer

Answer 21

yes

Answer 22

zero means "where does the function = 0". so you found both places

Answer 23

oh ok thank you very much for you help

Answer 24

np good luck!