Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

5, -3, and -1 + 2i

Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

5, -3, and -1 + 2i

hang254 · Answer

@ajprincess @SolomonZelman

kinggeorge · Answer

Do you remember what you have to do when you have an imaginary root (such as $-1+2i$)?

hang254 · Answer

not really, sorry

kinggeorge · Answer

No problem. It's fairly simple. All it is, is when you have an imaginary root (such as $-1+2i$), you have to have the complex conjugate as a root as well. In this case, the complex conjugate is $-1-2i$. So your polynomial will have 4 roots. Those will be$$5,\;-3,\;-1+2i,\;-1-2i.$$

kinggeorge · Answer

Next, we need to find the actual polynomial. To do this, multiply the 4 factors $x-r$ where $r$ is one of your roots. So in factored form, the polynomial will be$$(x-5)(x+3)(x-(-1+2i))(x-(-1-2i)).$$All you have to do is multiply these together one by one.

Hint: Multiply $(x-(-1+2i))(x-(-1-2i))$ first.

kinggeorge · Answer

It'll take a bit of work to do this final step. Let me know what you get at the end.