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

2, -4, and 1 + 3i

Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

2, -4, and 1 + 3i

anonymous · Answer

I know the other zero is 1 - 3i but I don't remember how to do this...

anonymous · Answer

... what are the zeros of (x-a)(x-b)(x-c) ta da ;D you got this

anonymous · Answer

$$(x-2)(x+4)(x-(1+3i))(x-(1-3i))$$

anonymous · Answer

the last pair is not hard, you can work backwards 
if the zero is $1+3i$ then you can write 
$$x=1+3i$$
$$x-1=3i$$
$$(x-1)^2=-9$$
$$x^2+2x+1=-9$$
$$x^2+2x+10=0$$

anonymous · Answer

or you can remember that if the zero is $a+bi$ the quadratic is 
$$x^2-2ax+a^2+b^2$$ either way

anonymous · Answer

i made a typo above, it is 
$$x^2-2x+10$$

anonymous · Answer

x^4 - 2x^2 + 36x - 80 ?

anonymous · Answer

yesh @allison_  good job