Find the zeros for the given polynomial function and give th

Find the zeros for the given polynomial function and give the mulitplicity for each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero.

f(x) = x^3 - 10x^2 + 25x

a. the set of zeros (use commas to separate answers)

b> multiplicity of the leftmost zero

c. multiplicity of the rightmost zero

d. does the leftmost zero cross or touch the x-axis and turn around?

e. does the rightmost zero cross or touch the x-axis and turn around?

Solution

given that f(x) = x^3 - 10x^2 + 25x

                         = x(x^2-10x+25)

                         = x(x-5)(x-5)

f(x) have zeros at x= 0 , 5

left most zero at x=0

right most zero at x=5

f(x) is zero , where the curve crosses the x-axis