Find the Polynomail Function, Given the Zeros 0, 1-√​3, and 4

[iv7]

Write a polynomial function in standard form and of the least degree that has a leading coefficient of 2 and the given zeros:

0, 1-√​3, 4

 

[mmm4444bot]

Write a polynomial function in standard form and of the least degree that has a leading coefficient of 2 and the given zeros:

0, 1-√​3, 4

What have you done, so far? Where did you get stuck? :cool:

 

[iv7]

I came up with an equation but when I put it into the graphing calculator, it was wrong. I came up with 2x^4-8x^3+8x^2+32x

 

[mmm4444bot]

I came up with [a polynomial] … 2x^4-8x^3+8x^2+32x

How did you come up with this polynomial? Did you use the given zeroes, in some way?

 

[iv7]

Yes, I expanded the factored form of 2x(x-4)(x-1√3)(x-1-√3)

 

[iv7]

I found the right answer.

 

[mmm4444bot]

I expanded the factored form of 2x(x-4)(x-1√3)(x-1-√3)

That's a typo, yes?

The factor ought to be (x - 1 + √3).

So, the expanded form is a fourth-degree polynomial:

f(x) = 2x^4 - 12x^3 + 12x^2 + 16x

The four zeros of this polynomial function are: 0 , 4 , 1 - √3 , 1 + √3


I found a lower-degree polynomial function.

It's zeros are the three given: 0 , 4 , 1 - √3

I found the right answer.

What did you eventually decide? :cool: