Question

Find the zeros of y = x2(x − 5)2(x − 3)4. State the multiplicity of multiple zeros.

Answer 1

\[y = x^{2} (x - 5)^{2}(x - 3)^{4}\]

this is a polynomial of order 2 + 2 + 4 = 8
so there are 8 zeroes but only 3 unique ones (each with multiplicity)

Answer 2

here is a hint. one zero is x = 0 because of the x^2 term. it has multiplicity 2