degree 4

Question

zeros i & (1+i)
constant term 12

How do I start this problem.

Thanks

A degree four polynomial will have the form (x^4 +... x + c), where c is a constant. You will need to generate an equation that has the above form, using c=12. Solve for the roots [i & (1+i)].

Answer 1

The equation would be:

x^4 + ax^3 + bx^2 + cx + 12 = 0

To solve for the coefficients a, b, and c, you can use the following equations:

a = -(i + (1+i))
b = i(1+i)
c = -12

Therefore, the polynomial is:

x^4 - (i + (1+i))x^3 + i(1+i)x^2 - 12x + 12 = 0