Find all zeroes of the function.
y = x^4 - 7x^2 + 12
To find the zeroes of the function, we set y to zero and solve for x:
0 = x^4 - 7x^2 + 12
Factoring the equation, we have:
0 = (x^2 - 3)(x^2 - 4)
Setting each factor equal to zero, we have two equations to solve:
x^2 - 3 = 0
x^2 - 4 = 0
Solving the first equation, we find:
x^2 = 3
Taking the square root of both sides, we have:
x = ±√3
Solving the second equation, we find:
x^2 = 4
Taking the square root of both sides, we have:
x = ±2
Therefore, the zeroes of the function are x = -2, -√3, √3, and 2.