1. satellite73

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

2. sugagal

zero of the polynomial function

3. sandra

is the first term x^2?

4. sugagal

yes

5. sandra

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

6. sugagal

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

7. sandra

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

8. sandra

exactly!

9. sugagal

thats as far as I got

10. sandra

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

11. sandra

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

12. sandra

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

13. sandra

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

14. sandra

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

15. sandra

so you can do that =)

16. sugagal

-4

17. sugagal

x=-4

18. sandra

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

19. sandra

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

20. sugagal

ok, so is that the answer

21. sandra

yes

22. sandra

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

23. sugagal

oh ok thank you very much for you help

24. sandra

np good luck!

Find more explanations on OpenStudy