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.

✔ crossesX does not intersecttouches

crossesdoes not intersect✔ touches

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).

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

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

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

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 ⇒ 2 roots.

f (x) = (x2 + 6)2 has ⇒ 4 roots.

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