The problem is based on the properties of the graphs of polynomial functions. First of all degree is odd and as x tends to infinity, y tends to negative infinity, therefore the graph of the polynomial function will rise to the left and fall to the right. This implies that the leading coefficient of the polynomial must be negative. As the polynomial has real multiple roots and also since y intercept has to be negative, the graph should cross x axis only on the left of the origin. With these characteristics in consideration we can write a polynomial with at least two roots of odd multiplicity as follows:

Y= -((x+3)³(x+1)³(x+2), Or f(x)= -x⁷-14x⁶-81x⁵-250x⁴-443x³-450x²-243x-54. The graph of this function is reproduced below for easy understanding. There can be any number of polynomial functions like this