The Fundamental Theorem of Algebra Answers

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).

Use the fundamental theorem of algebra to determine the number of roots for each polynomial function shown.f (x) = 2x3 + x2 - 7x + 1 has ⇒ 3 roots.

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

This function has roots.

Complete the steps to find all zeroes of the function f(x) = x4 − 4x3 − 4x2 + 36x − 45. This function has roots. The possible rational roots are ±1, ±3, ±5, ±9, ±15, and ±45. The actual roots ordered from least to greatest are and .

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

There are two roots because of the X negative radicand.nonperfect square radicand.✔ need to identify + and - roots of the radicand.

f (x) = -3x + 5x2 + 8 has ⇒ 2 roots.

The actual roots ordered from least to greatest are and .

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 ✔ negative radicand.nonperfect square radicand.X need to identify + and - roots of the radicand.

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

The function has real roots and imaginary roots.

-2 + i and -2 - i ✔ 2 + i and 2 - i 4 + 2i and 4 - 2i 2 + 4i and 2 - 4i

Complete the steps to find all zeroes of the function f(x) = x4 − 4x3 − 4x2 + 36x − 45. This function has roots. The possible rational roots are ±1, ±3, ±5, ±9, ±15, and ±45. The actual roots ordered from least to greatest are and .