Question

What is a quartic function with only the two real zeros given?

x = -4 and x = -1

A. y = x4 + 5x3 + 5x2 + 5x + 4

B. y = x4 - 5x3 - 5x2 - 5x - 4

C. y = -x4 + 5x3 + 5x2 + 5x + 4

D. y = x4 + 5x3 + 5x2 + 5x - 5

Answer 1

@Forever_Me
@rajee_sam

Answer 2

For this, the factors must be (x+1)(x+4) to make it equal zero at both indicated values.

Answer 3

I didn't get it

Answer 4

@Numb3r1

Answer 5

he is asking for Quartic function
it has only 2 real zeros

Answer 6

To make x=-4 and x=-1 give zero when fed through the function, (x+1)(x+4) must be the factorization of the equation. There must also be either a quadratic equation without any real zeros or more of those same factors.

Answer 7

So other 2 are complex

Answer 8

All I can think of is use synthetic division to divide all the 4 answer choices to see which one has both -1 and -4 as its zeros and then examine the quotient to see which one has complex roots

Answer 9

he is asking which eqution has only the givin zeros -1 -4

Answer 10

It isn't too hard to multiply those factors, then use synthetic division to test that. It'll save a little bit of work that way.

Answer 11

It is very laborious but I cannot think of any other way now.

Answer 12

I'd divide by the quadratic, is what I'm saying. It saves a step of division.

Answer 13

guys I really don't know how to do this so can u help me figure out what is the answer

Answer 14

I cannot do synthetic then, I would have to do long division once I multiply them.

Answer 15

Ok do you know how to do synthetic division?

Answer 16

Why not? It's one division instead of two.

Answer 17

I'm really confused

Answer 18

Once you multiply the two factors it will be a trinomial. Can I do synthetic with a trinomial divisor?

We will help you out malka in a bit just hang on. Thinking of a less tedious way to do it.

Answer 19

you would have to do the long division

Answer 20

Ok here is what we will do. If x=-4 and x=-1 are zeroes. Then x+4 and x+1 are factors . Do you agree @malkassir

Answer 21

yes

Answer 22

So now multiply those.

Answer 23

Now let us multiply the two together : (x+1)(x+4) = x^2 + 5x + 4

Answer 24

ok

Answer 25

Now we're going to do long division:

Answer 26

Now take that and divide all the 4 answer choices. Once you divide it should divide completely without a remainder because they are a factor

Answer 27

Here are your original options:
A. y = x4 + 5x3 + 5x2 + 5x + 4

B. y = x4 - 5x3 - 5x2 - 5x - 4

C. y = -x4 + 5x3 + 5x2 + 5x + 4

D. y = x4 + 5x3 + 5x2 + 5x - 5

Answer 28

@Numb3r1 , I will do A and show him how to do it.

Answer 29

okay I will do B
and @Numb3r1 you do c
and we will see which one is right

Answer 30

Here's a drawing to start all of them off: