Create A Polynomial Function

[mathdad]

Given zeros: -1, 1, 3; degree 3, find a polynomial function.

Solution:

f(x) = a(x - r)(x - 1)(x - r)

I will use x - r by replacing r with the given zeros.

Let r = -1, 1, 3, respectively in terms of x - r.

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

The leading coefficient for this polynomial function is 1. Thus, a = 1.

Correct?

 

[Romsek]

Yes, this is correct.

 

[MarkFL]

Well, the family of 3rd degree polynomials meeting the given criteria could be given as:

[MATH]f(x)=a\left(x^3-3x^2-x+3\right)[/MATH] where \(a\ne0\)

You have chosen \(a=1\) to get one member of that family, but you aren't required to choose this particular one.

Also, for clarity, you should replace:

f(x) = a(x - r)(x - 1)(x - r)

with:

[MATH]f(x)=a\left(x-r_1\right)\left(x-r_2\right)\left(x-r_3\right)[/MATH]

 

[mathdad]

Yes, this is correct.

Another one for my notes.

 

[mathdad]

Well, the family of 3rd degree polynomials meeting the given criteria could be given as:

[MATH]f(x)=a\left(x^3-3x^2-x+3\right)[/MATH] where \(a\ne0\)

You have chosen \(a=1\) to get one member of that family, but you aren't required to choose this particular one.

Also, for clarity, you should replace:

f(x) = a(x - r)(x - 1)(x - r)

with:

[MATH]f(x)=a\left(x-r_1\right)\left(x-r_2\right)\left(x-r_3\right)[/MATH]

I got it. Thanks.