Question

# Find the polynomial function k(x) of lowest degree in standard form if it has roots: x=1,3,2i

Answer

k(x) = (x-1)(x-3)(x^2 + 4)

- Q:What are the roots of the polynomial? A:The roots are x=1,3,2i.
- Q:What is the standard form of the polynomial? A:The standard form of a polynomial is to multiply the factors (x-a)(x-b)(x-c)...where a,b,c are the roots. So the standard form of this polynomial is k(x) = (x-1)(x-3)(x-2i)(x+2i), and it needs to be simplified.
- Q: How can we simplify k(x)? A:We can simplify k(x) by multiplying the complex conjugate (x-2i)(x+2i) to get rid of the imaginary part. So we get k(x) = (x-1)(x-3)(x^2 + 4), which is the simplified standard form of k(x).