Question

Find the zeros of the polynomial function.

f(x) = x3 + 5x2 - 4x - 20

Answer 1

A. x = -5, x = 4

B. x = -2, x = 2

C. x = -5, x = -2, x = 2

D. x = 5, x = -2, x = 2

Answer 2

@Umangiasd ?

Answer 3

The easiest way, when you have possibilities is try 'em on,
let's try answer A
f(-5)=-125+125+20-20=0, so x=-5 is a zero of the polyn..
now, if x=4
f(4)=64+80-16-20=118, so x=4 is not a zero, let's keep trying on ;)

Answer 4

i dont have a calc by me :(

Answer 5

ans im not fully crasping what your doing

Answer 6

evaluate, just replace the x for what your answer says, for example
f(x)=x^3 + 5x^2 - 4x - 20
f(-2)=(-2)^3+5(-2)^2-4(-2)-20
f(-2)=-8 +5*4-(-8)-20=-8+20+8-20=0
do you get it now? (and you don't need a calculator)

Answer 7

but i dont get what im looking for the answer to be?

Answer 8

0, they're asking you for the zeros of the polynomial func

Answer 9

i didnt C and D on paper and i got C?

Answer 10

f(x) = x^3 + 5x^2 - 4x - 20
f(x) = x^2(x + 5) - 4(x + 5)
f(x) = (x^2 - 4)(x + 5)

When f(x) = 0
0 = x^2 - 4
0 = x + 5

You should be able to solve the rest from there.

Answer 11

To me, that's the easiest way

Answer 12

actually @Hero you got me confused

Answer 13

I'm sorry to hear that

Answer 14

@Umangiasd, what do you think?

Answer 15

I insist, the easiest way to achieve it is to evaluate the functions and see for which x do i get 0 as a result
The mathematical correct way is yours, but requires a strong knowledge of factorization, the first case is just evaluate a function ^^!

By the way, @ErinWeeks if f(x)=x+2, how much is f(x) if x=-2

Answer 16

Well, the factorization took about a minute. For the evaluation method, you might need a calculator which @erinweeks doesn't have.

Answer 17

i insist, in this case, you don't need a calculator for numbers below 10, c'mon xD

Answer 18

lol, true....just teasing

Answer 19

Nevermind I'll go else where thanks

Answer 20

Where else are you going to go?

Answer 21

To get some other help !!(:

Answer 22

I used the factor by grouping method @erinweeks

Answer 23

You may have heard of it before.

Answer 24

Just forget it .. thank you

Answer 25

If you go elsewhere to get help, chances are, they'll show you one of either methods @Umangiasd and I have already shown.

Answer 26

@ErinWeeks what is the issue you have with what you've been given here? Tell us what you don't understand or like...

Answer 27

You're asked to find the zeros (aka roots) of the equation. Those are the values of x that make the polynomial = 0. The first person suggested that as you have a multiple choice question, you could just try the various answers and see which one works. The other person told you how you could solve the problem without having the answers. I can tell you another way to find the answers if you want, but if the first two were too confusing, I'm afraid you won't find the other way an improvement.

Answer 28

One point that I didn't notice being made is that this is a polynomial with x^3 as the highest power. This means that there will be 3 zeros. You can immediately discard any answer choices that do not have 3 zeros.

Answer 29

That leaves you with two sets of zeros to try out in the equation. Even if it takes you a minute to try each one, you should be done in 5 minutes or less. The numbers are pretty easy on this one, so it shouldn't even take that long.

Answer 30

If you have quite a few numbers to try, or aren't very good at arithmetic, you might try a process called synthetic substitution. There's a decent explanation at http://hanlonmath.com/pdfFiles/29.SyntheticSubstitution.pdf

It's also known as Horner's method, and is a more efficient way to evaluate a polynomial than the obvious way (few multiplications involved, and the numbers tend to stay a bit smaller). It takes a little practice to master, but in my opinion (which I'm sure you won't want to hear), just about everything in a typical math class is a good candidate for some extra practice, and not wanting to do it is a prima facie indication that you ought to.