Aim #17: How do we find the equation of a polynomial given imaginary
roots?
HW Packet Due Monday 10/17
Test (Aims 1-17) Tuesday 10/18
Do Now :
Write the equation of a 4th degree polynomial with zeros at -1, 2, 3 and 5
Write the equation of a 5th degree polynomial with zeros at -2, 2, and 5
Write the equation of a 3rd degree polynomial with zeros at 1 and -i
RECALL:
Complex Conjugates:
Let f(x) be a polynomial that has real coefficients.
If a + bi is a zero of the function, b ≠ 0, then the conjugate
a - bi is also a zero of the function.
So if you are given 2 - 3i as a root of a polynomial,
what else MUST be a root?
What if 4i and -4 + i are roots of a polynomial, what else
MUST be roots?
Find a fourth degree polynomial with real coefficients
that has 2, 3 and 4i as zeros.
Now what if you were asked to find all roots of a polynomial
given a root or factor, but this time it is complex?
Find all zeros of f(x) = x3 + x2 + 9x + 9 given that 3i is a zero.
Find a fourth degree polynomial with real coefficients
that has -4, 5 and -2 - √-9 as zeros.
Find all zeros of f(x) = x4 - x3 + 3x2 - 4x - 4 given that -2i is a zero.
Find a forth degree polynomial with real coefficients
that has -1, 4 and 2i as zeros.
Find a fourth degree polynomial with real coefficients
that has -3, 3 and 1 + √-25 as zeros.
Find a fifth degree polynomial with real coefficients that
has -2, 4i and -3-2i as zeros.
3
2
Find all zeros of f(x) = x - 5x + 16x - 80 given that 4i is a
zero.