Question

Hich of the following are solutions of t⁴ - 16 = 0?

a) t = 2
b) t = -2
c) t = -1
d) t = 1

Answer 1

The solutions to the equation t⁴ - 16 = 0 are t = 2 and t = -2, which are derived from factoring the difference of squares. Options t = -1 and t = 1 are not solutions.

Step-by-step explanation:

Finding Solutions to Polynomial Equations

To determine which of the options given are solutions to the equation t⁴ - 16 = 0, we can first factor the equation. Factoring a difference of squares, we get:

(t² + 4)(t² - 4) = 0

This further breaks down into:

(t + 2)(t - 2)(t² + 4) = 0

So the real number solutions for t are t = 2 and t = -2. The equation t² + 4 = 0 does not have real number solutions because the sum of a square and a positive number cannot be zero.

Thus, the correct answers from the provided options are:

t = 2

t = -2

Options t = -1 and t = 1 are not solutions to the equation.