Question

What are the zeroes of the function? What are their multiplicities?

Answer 1

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.