The equation is x^4 - 4x^3 + 3x^2 = 0.
You can simplify the terms as so:
x^2(x^2-4x+3) = 0
The equation above now contains x^2 and a quadratic function. A potential solution is x = 0 because x^2 = (0)^2 = 0.
Regarding the quadratic part of the equation,
x^2 - 4x + 3 = 0
(x+4)(x-1) = 0
When x = -4 or 1, the entire equation equals zero.
Therefore, the zeroes of the function are -4, 0, and 1.