Writing Polynomial Functions from Complex Roots
If a polynomial function f(x) has roots 4 - 13i and 5, what must be a factor of f(x)?
(x - (4 + 13i))
Which polynomial function f(x) has a leading coefficient of 1, roots -4, 2, and 9 with multiplicity 1, and root -5 with multiplicity 3?
f(x) = (x + 5)(x + 5)(x + 5)(x + 4)(x - 2)(x - 9)
What is the polynomial function of lowest degree with lead coefficient 1 and roots i, -2, and 2?
f(x) = x⁴ - 3x² - 4
Which polynomial function has a leading coefficient of 1 and roots 2i and 3i with multiplicity 1?
f(x) = (x + 2i)(x + 3i)(x - 2i)(x - 3i)
Which second degree polynomial function has a leading coefficient of -1 and root 4 with multiplicity 2?
f(x) = -x² + 8x - 16
Which polynomial function has a leading coefficient of 3 and roots -4, i, and 2, all with multiplicity 1?
f(x) = 3(x + 4)(x - i)(x + i)(x - 2)
If a polynomial function f(x) has roots 0, 4, and 3+√11, what must also be a root of f(x)?
3 -√11
If a polynomial function f(x) has roots -9 and 7 - i, what must be a factor of f(x)?
(x - (7 + i))
If a polynomial function f(x) has roots -8, 1, and 6i, what must also be a root of f(x)?
-6i
A factor of the polynomial function f(x) shown in the graph is (x - 1).
Graph of f(x)
A factor of the polynomial function f(x) shown on the graph is (x + 6)
Graph of f(x)
This polynomial function f(x) = -2x³ - 2x² + 12x could be represented by the graph.
Graph of f(x)
This polynomial function f(x) = 3x² - 18x + 24 could be represented by the graph.
Graph of f(x)