Question

Find the roots of P(x)=x(x+2)^2(x-1)^3(2x-3) and state the multiplicities of each root.

Answer 1

The roots of the polynomial P(x) = x(x+2)^2(x-1)^3(2x-3) are x = 0, x = -2, x = 1, and x = 3/2, with multiplicities 1, 2, 3, and 1, respectively.

Step-by-step explanation:

The roots of the polynomial P(x) = x(x+2)^2(x-1)^3(2x-3) can be found by setting each factor equal to zero and solving for x. The roots are:

x = 0 (multiplicity 1)

x = -2 (multiplicity 2)

x = 1 (multiplicity 3)

x = 3/2 (multiplicity 1)