The Fundamental Theorem of Algebra Answers

Use the fundamental theorem of algebra to determine the number of roots for each polynomial function shown.f (x) = 2x3 + x2 - 7x + 1 has roots.

f (x) = -3x + 5x2 + 8 has roots.

f (x) = (x2 + 6)2 has roots.

For the single roots −1 and 2, the graph the x–axis at the intercepts.

For the double root 3, the graph the x–axis at the intercepts.

Describe the graph of the function g(x) = (x − 1)(x + 4)3(x + 5)2. The graph: the axis at (1, 0). the axis at (−4, 0). the axis at (−5, 0).

Describe the graph of the function g(x) = (x − 1)(x + 4)3(x + 5)2. The graph: the axis at (1, 0). the axis at (−4, 0). the axis at (−5, 0).

Describe the graph of the function g(x) = (x − 1)(x + 4)3(x + 5)2. The graph: the axis at (1, 0). the axis at (−4, 0). the axis at (−5, 0).

h(x) = 2x2 + 26The fundamental theorem of algebra tells you that this polynomial function has roots.

Solve 2x2 + 26 = 0 to identify the roots.

When solving, you took the square root of both sides of the equation. Consider this step when completing the following statements. The roots are imaginary because of the

There are two roots because of the

This function has roots.

The actual roots ordered from least to greatest are and .

The actual roots ordered from least to greatest are and .

x =

The function has real roots and imaginary roots.

The function has real roots and imaginary roots.