Help with polynomial of a given degree with given zeros.

Algebra
Tutor: None Selected Time limit: 1 Day

Find a polynomial f(x) of degree 3 with real coefficients and the following zeros.

-1 , 2i

Simplify completely including i's.

Oct 17th, 2015

Hello!

If a polynomial has zero a, it can be expressed as (x-a)*(some other polynomial). Also, if a polynomial with real coefficients has a complex (non-real) root z, then the conjugate of z is also its root. Conjugate of 2i is -2i.

So, p(x) = a*(x+1)*(x-2i)*(x+2i) = a*(x+1)*(x^2+4) = a*(x^3+x^2+4x+4).
Here a is any real number except 0.

Please ask if something is unclear.
Oct 17th, 2015

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