Find all real and/or imaginary solutions. x^4+5x^2−14=0
To find the solutions, let's first substitute a variable to simplify the equation.
Let u = x^2.
Then the equation becomes:
u^2 + 5u - 14 = 0.
Now we can solve for u using factoring or the quadratic formula.
Factoring:
(u + 7)(u - 2) = 0.
Setting each factor equal to zero:
u + 7 = 0 or u - 2 = 0.
Solving for u:
u = -7 or u = 2.
Substituting back for x:
x^2 = -7 or x^2 = 2.
Taking the square root of each side:
x = ±√(-7) or x = ±√2.
Therefore, the real solutions are x = ±√2, and the imaginary solutions are x = ±√(-7).