OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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)

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago