Question 835397
Question:
Q has degree 3 and zeros -5 and 1+i. find a polynomial that satisfies the given conditions.
----------------------------------------------------
Answer:
If 1 + i is a root of Q, then its conjugate, 1 - i is also a root.
Sum of imaginary roots: (1 + i) + (1 - i) = 2
Product of imaginary roots: (1 + i)(1 - i) = 2
Quadratic Equation: {{{x^2 - (sum)x + product = 0}}}
{{{x^2 - 2x + 2 = 0}}}
Cubic Equation: {{{(x^2 - 2x + 2)(x + 5) = 0}}} or
{{{x^3 + 3x^2 - 8x + 10 = 0}}}
The polynomial function is {{{highlight(Q(x) = x^3 + 3x^2 - 8x + 10)}}}