find poly w/ degree 3, zero at x=-3, x=4 is zero of mult. 2,

[vegettass2]

Im suppose to find the polynomials with the following characteristics:
- the degree is 3
- the coefficient of the x terms is -24
- -3 is a zero
- 4 is a z zero of multiplicity 2

so........ this is what i think the question is... -24x^3 - 3 + (x-4)^2 ?

 

[stapel]

Im suppose to find the polynomials with the following characteristics:
- the degree is 3
- the coefficient of the x terms is -24

The coefficient of each of the terms is -24...? Or the leading coefficient is -24...?

- -3 is a zero
- 4 is a z zero of multiplicity 2

so........ this is what i think the question is... -24x^3 - 3 + (x-4)^2 ?

Um... no. :shock:

To learn how to find polynomials from their zeroes, try here. :wink:

 

[vegettass2]

Re:

The coefficient of each of the terms is -24...? Or the leading coefficient is -24...?

it just said what i typed earlier in th question. i just needs help putting the words into an equation...
anyway i came up with something else...

is this what the words suppose to be??
x^3-24x+(x+3)+(x-4)^2

n this'll end up with the x^3+x^2-31x+19?

 

[vegettass2]

Im suppose to find the polynomials with the following characteristics:
- the degree is 3
- the coefficient of the x term is -24
- -3 is a zero
- 4 is a z zero of multiplicity 2

so........ this is what i think the question is... -24x^3 - 3 + (x-4)^2 ?

sorry i had a S on the term before.

 

[Mrspi]

Im suppose to find the polynomials with the following characteristics:
- the degree is 3
- the coefficient of the x terms is -24
- -3 is a zero
- 4 is a z zero of multiplicity 2

so........ this is what i think the question is... -24x^3 - 3 + (x-4)^2 ?

If -3 is a 0, then (x - -3) or (x + 3) is a factor of the polynomial.

If 4 is a zero of multiplicity 2, then (x - 4)^2 is a factor of the polynomial

You can express the polynomial function as

f(x) = a (x + 3)(x - 4)^2

Expand the right side:

f(x) = a(x - 3)(x^2 - 8x + 16)
f(x) = a(x^3 - 11x^2 + 48x - 48)
f(x)= ax^3 - 11ax^2 + 48ax - 48a

Now...you are told that the coefficient of the x term is -24. And, we can see that the coefficient of the x term in the expansion is 48a....

So,
48a = -24
a = -24/48, or
a = -1/2

Looks to me like the polynomial function is

f(x) = (-1/2)*(x - 3)(x - 4)^2