Question

Solving Expressions Analytically Consider the following equation: x3+4x2+4x+16=0. Solve for x. Your answer should be stored in a variable result, which will be a list containing three sympy expressions.

Answer 1

Answer:

List is {-2i, 2i, -4)

Step-by-step explanation:

This is a third order polynomial, so we expect three roots (solutions).

Note that we can factor this expression by grouping:

(x²)(x + 4) + (4)(x + 4) = 0, or

(x + 4)(x² + 4) = 0

The factor (x + 4) corresponds to the root/solution x = -4, and:

The other factor (x² + 4) corresponds to the roots/solutions x = 2i and x = -2i.

List is {-2i, 2i, -4)