Question

What are the solutions of the equation x^4 + 95x^2 - 500= 0? Use factoring to solve

Answer 1

1) given x^4 + 95x^2 - 500

2) split in two factors with common factor term x^2: (x^2 + )(x^2 - )

3) find two numbers that add up 95 and their product is - 500:

=> 100*(-5) = - 500 and 100 - 5 = 95

=> (x^2 + 100)(x^2 - 5)

4) factor x^2 - 5 = (x + √5) (x - √5)

5) write the prime factors: (x^2 + 100) (x + √5) (x -√5)

6) find the solutions:

x^2 + 100 = 0 => not possible

x + √5 = 0 => x = - √5

x - √5 = 0 => x = √5


Answer: x = √5 and x = - √5