Find all the zeros in the equation
12x^2-64=-x^4
To find the zeros of the equation, we need to set it equal to zero. So, we rewrite the equation as:
x^4 + 12x^2 - 64 = 0
Now, let's solve this equation for x. We can factor this equation as a quadratic in terms of x^2:
(x^2 + 16)(x^2 - 4) = 0
Now we have two equations to solve:
1) x^2 + 16 = 0
Subtracting 16 from both sides:
x^2 = -16
Taking the square root of both sides (remembering that the square root of a negative number is imaginary):
x = ±4i
Therefore, the zeros of this equation are x = 4i and x = -4i.
2) x^2 - 4 = 0
Adding 4 to both side:
x^2 = 4
Taking the square root of both sides:
x = ±2
Therefore, the zeros of this equation are x = 2 and x = -2.