Question

Write a polynomial P(x) of degree 5 and with zeros 2, 5/2, (which of multiplicity one) and 0 (of multiplicity 3). Note: if x-c is a zero of P(x) of multiplicity k, then (x-c)^k is a factor of P(x)

Answer 1

We have the following:

$x^3\cdot(x-2)\cdot(x-\frac{5}{2})=0$