The graph below is a polynomial function in the form fx x a

The graph below is a polynomial function in the form f(x) = (x -a)^2(x- b)(x - c). Find suitable unique real numbers a, b, and C that describe the graph., A cubic polynomial with negative leading coefficient is shown for -10

Solution

1) we can see th graph touches the x axis at x=- 2 which means it has zero of multiplicity 2

Further graph cuts the x axis at x =1 , 3

So, f(x) = ( x+2)^2(x-1)(x-3)

a = -2, ; b = 1; c = 3

2) The graph cuts the x axis at two points, so f(x) has two zeros

-5<x < 0 --- one zero

0<x<5 ---- one zero