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

@SolomonZelman @phi

Answer 2

@ParthKohli

Answer 3

From the given roots, the polynomial can be factored to look like this:
\[(x-2)(x+4)(x-(1+3i))\]
As is, if you were to expand it, you'd have some complex coefficients.

To rectify that, recall that complex roots come in conjugate pairs, so \(1-3i\) is also a root, and you have
\[(x-2)(x+4)(x-(1+3i))(x-(1-3i))\]
Expand and write in standard form.

Answer 4

@SithsAndGiggles how would I write it in standard form?

Answer 5

Standard form of a polynomial of degree \(n\) is
\[a_nx^n+a_{n-1}x^{n-1}+\cdots+a_2x^2+a_1x+a_0\]
So for example, if you have \(f(x)=(x-1)(x+1)\), then standard form is obtained by expanding:
\[f(x)=x^2-x+x-1=x^2-1\]

Answer 6

http://www.wolframalpha.com/input/?i=expand+%28x%E2%88%922%29%28x%2B4%29%28x%E2%88%92%281%2B3i%29%29%28x%E2%88%92%281%E2%88%923i%29%29