Question

What are the solutions of the equation x⁴ - 5x² - 14 = 0? Use factoring to solve.

A) x = 7 and x = -7
B) x = 7i and x = -7i
C) x = 1/7 and x = 12
D) x = 7 and x = -7

Answer 1

To solve the equation x⁴ - 5x² - 14 = 0 using factoring, we can treat it as a quadratic equation in terms of x². By factoring the quadratic equation, we find the solutions x = √7 and x = -√7.

Step-by-step explanation:

To find the solutions of the equation x⁴ - 5x² - 14 = 0 using factoring, we can treat it as a quadratic equation in terms of x². Let's denote x² as y. The equation becomes y² - 5y - 14 = 0. Now we can factor this quadratic equation:

(y - 7)(y + 2) = 0

This gives us two possible values for y: y = 7 or y = -2. Since y represents x², we can take the square roots of these values to find the solutions for x:

x = √7 or x = -√7