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

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

anonymous · Answer

the first part is routine 
$$(x-4)(x+2)$$ it is the second part that requires work, but i can show you a snap  way to do it if you like

anonymous · Answer

one way to find the quadratic with zero at $-1+2i$ is to work backwards 
put 
$$x=-1+2i$$ add 1 get 
$$x+1=2i$$ square and get 
$$(x+1)^2=-4$$ or 
$$x^2+2x+1=-4$$ or 
$$x^2+2x+5$$ that is your quadratic

anonymous · Answer

the real snappy way is to memorize that if $a+bi$ is the zero of a quadratic, the equation is 
$$x^2-2ax+(a^2+b^2)$$

anonymous · Answer

ok this was such a big help so you just multiplied like terms and then broke down the 2i andi just did it on paper and got x^2-2x-8 the first part of (x-4)(x+2)

anonymous · Answer

i got -4x^2+8x+32 as the answer, correct?

anonymous · Answer

i made an error, my final answer is f(x) = x4 - 7x2 - 26x - 40