What is the standard form of a polynomial function with given roots and degree?

[thomasrules]

The Roots and degree of a polynomial function are given. Write the function in standard form.

b) 2, -2i, degree 4

obviously i know there is a function with x^4 and it should have 4 x answers so I don't know how to do this...I know that (x-2) is a factor

 

[dmoravec]

then what about (x+2i) and who says that 2 can only be a root once? What about -2i?

 

[StatusX]

Does the polynomial have to be real? If so, note the roots must come in complex conjugate pairs. If not, just multiply together the right number of factors of (x-r), where r is a root.

 

[thomasrules]

yes it has to be real

 

[dmoravec]

then statusX is saying if -2i is a root, then 2i must be a root as well, since 2i is the complex conjugate of -2i [the complex conjugent of a+bi is a-bi, you just have no a in this situation]

 

[thomasrules]

SO IT'S

(x-2)(x+2)(x+2i)(x-2i)

 

[HallsofIvy]

I am confused. The problem says "The Roots and degree of a polynomial function are given" and I would interpret "The Roots" to mean that the the polynomial has only those roots. However, then it couldn't have real coefficients.

If the polynomial has real coefficients and then the roots given are not all. Clearly -2i must be another but the fourth could be any real number. There are an infinite number of solutions: (x-a)(x-2)(x²+4) where a is any real number.