Consider the following graph of a polynomial function What i

Consider the following graph of a polynomial function. What is the minimum degree of the polynomial ? What are the zeros (roots) of the function ? What are the factors of the polynomial function ? For what intervals of x, is f(x)> 0?

Solution

i)We can see from the graph that curve cuts the x axis at x= -3 and touches the x axis at x=3

So, degree of polynomial = 1 + 2 ( multiplicity 2 as at x=3 curve touches the axis)

= 3

ii) Zeros are x= -3 , x= 3 ,x =3

iii) Factors of polynomial : f(x) = k(x- 3)^2(x+3)

iv) f(x) >0 .Looking at graph we can see that : f(x) >0 for ( -3 , 3) U ( 3, +infinity)