The given word contain the root -flict-. Using the definition, explain how the root contributes to the meaning of the given word.

inflict: to give or cause pain

Use DeMoivre’s Theorem to verify the indicated root of the real number. $-\frac{1}{2}(1+\sqrt{3} i)$ is a sixth root of 1

Write an equation for a fourth-degree polynomial that has a double root at x = -3, a complex root of x = 1 - 2i, and passes through the point (2, -25).

Apply the Root Test to determine convergence or divergence, or state that the Root Test is inconclusive.

$$\sum _ { n = 1 } ^ { \infty } \left( \frac { 3 } { 4 n } \right) ^ { n }$$

Find the root.

$$\sqrt[5]{256}$$

Are cube root functions even or odd?

In this exercise, make the given changes in the indicated examples of this section and then solve the given problems.

In Example $2(b)$, change the square root to a cube root and then evaluate.

The given word contain the root -flict-. Using the definition, explain how the root contributes to the meaning of the given word.

affliction: the condition of pain or suffering

For the following exercise,

Evaluate each root.

Evaluate the cube root of $z$ when $z=32 \operatorname{cis}\left(\frac{2 \pi}{3}\right)$.

Prove that

$$f ( x ) = x ^ { 4 } + 5 x ^ { 3 } + 4 x$$

has no root c satisfying c > 0. Hint: Note that x = 0 is a root and apply Rolle's Theorem.

Which of the following statements is true?

• a. The GRUB boot loader is stored in the /usr/grub directory.
• b. LILO needs to be reinstalled after it has been modified.
• c. The GRUB2 boot loader is often used on legacy Linux systems.
• d. GRUB needs to be reinstalled after it has been modified.

Study the entries and answer the question that follows.

The root plic means "fold."

The root lig means "connect" or "bind."

The root solv means "loosen."

The prefix ex-means "out."

The prefix re- means "back" or "again."

The prefix ab- means "away from."

The prefix ob - means "toward" or "against."

List as many words as you can think of that contain the root solv.

Identify the below statement about a root as true or false.

Many words contain more than one root.

$$\mathrm{T}\quad\mathrm{F}$$

Study the entries and answer the question that follows.

The root pol means "city."

The root civ means "citizen."

The root urb means "city."

The prefix mega- means "large."

The prefix sub- means "under."

The prefix metro- means "mother." What, literally, is a metropolis?