Decide which of the polynomial functions in the might have t

Decide which of the polynomial functions in the might have the graph below. (More than one answer may be possible.) (a)y=-4x(x-1)(x-2) (b) y = x2(x-1 )2(x-2) (c) y = 3x(x- 1)(x-2) (d) y = x(x-1)2(x-2)2 (e) y = 3x(1 -x)(2-x) (f)y=-x(1-x)(x-2) Which of the polynomial functions in the list might have the given graph?

Solution

This can be solved by simple root

If there is odd power at x=x\' ---> sing of f(x) will change across x\'
so,
x\'= 0 should have odd power
as for x<0, f(x) is negative and for x>0, it is positive

If there is even power at x=x\' ---> sing of f(x) will not change across x\'
so,
x\'= 1 and x\'=2 should have even power

Answer: d