Question

What are the solutions of the equation x^4 – 5x^2 - 5x^4 - 14 = 0? Use factoring to solve.

a) x = ±7 and x = √14
b) x = 1/7 and x = -√14
c) x = ±i7 and x = √14
d) x = ±√7 and x = -i√14

Answer 1

The given equation x^4 - 5x^2 - 5x^4 - 14 = 0 simplifies to a quadratic equation that does not have real solutions, as its discriminant is negative. Therefore, none of the given options are correct.

Step-by-step explanation:

The solutions of the equation x^4 – 5x^2 - 5x^4 - 14 = 0 can be found by combining like terms and then using factoring to solve the resulting quadratic equation. First, combine the x^4 and -5x^4 terms to simplify the equation to -4x^4 - 5x^2 - 14 = 0. Next, factor out a '-1' which gives us 4x^4 + 5x^2 + 14 = 0. This does not factor nicely, and since it's a bi-quadratic equation, we can set y = x^2 to get a quadratic in terms of y: 4y^2 + 5y + 14 = 0. Unfortunately, this quadratic does not have real solutions because the discriminant (b^2 - 4ac) is negative. Therefore, we will not have real solutions for x either, as they would be the square roots of the solutions for y. In conclusion, this equation does not have real solutions and the given options do not apply.