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

4, -2, 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.

4, -2, and -1 + 2i

anonymous · Answer

f(x) = x4 - 3x3 + 8x2 + 13x + 40

correct

anonymous · Answer

start with 
$$(x-4)(x+2)(x-(-1+2i))(x-(1-2i))$$ and multiply out 
but before we being the last product is very easy

anonymous · Answer

can you kinda go back words with me  work best that way please and thanks

anonymous · Answer

if the zeros are $a+bi$ and $a-bi$ the quadratic is 
$$x^2-2ax+(a^2+b^2)$$
in your case it is 
$$x^2+2x+5$$

anonymous · Answer

ok lets start at the very beginning

anonymous · Answer

if $-1+2i$ is a zero, then so is its conjugate  $-1-2i$

anonymous · Answer

the quadratic equation that will have those two zeros is 
$$x^2+2x+5$$ 
is it clear how i got that?

anonymous · Answer

rightt i got that

anonymous · Answer

oh ok good
then your final job is to multiply out 
$$(x-4)(x+2)(x^2+2x+5)$$

anonymous · Answer

f(x) = x4 - 7x2 - 26x - 40

anonymous · Answer

you can do it in any order you like , but as you can see it is a bunch of algebra you have to do.
yes, that is correct

anonymous · Answer

thankkkksss

anonymous · Answer

yw, it looks like you did it on your own
good job