Find all real and/or imaginary solutions. Show you work.
x^4 + 5x^2 -14 = 0
A. x = ±√3i or x = ±√6
B. x = ±√6i or x = ±√3
C. x = ±√2i or x = ±√7
D. x = ±√7i or x = ±√2
To solve for x, we can use a substitution. Let's substitute y = x^2. Then the equation becomes y^2 + 5y - 14 = 0.
To solve this quadratic equation, we can factor it as (y + 7)(y - 2) = 0.
Setting each factor equal to zero, we have y + 7 = 0 or y - 2 = 0.
For y + 7 = 0, solving for y, we have y = -7.
For y - 2 = 0, solving for y, we have y = 2.
Now we substitute y back into the equation y = x^2.
For y = -7, we have x^2 = -7.
Taking the square root of both sides, we have x = ±√7i.
For y = 2, we have x^2 = 2.
Taking the square root of both sides, we have x = ±√2.
Therefore, the solutions are x = ±√7i or x = ±√2.
The correct answer is D. x = ±√7i or x = ±√2.