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

Answer 1

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

Answer 2

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

Answer 3

\[(x-2)(x+4)(x-(1+3i))(x-(1-3i))\]

Answer 4

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

Answer 5

or you can remember that if the zero is \(a+bi\) the quadratic is
\[x^2-2ax+a^2+b^2\] either way

Answer 6

i made a typo above, it is
\[x^2-2x+10\]

Answer 7

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

Answer 8

yesh @allison_ good job