SOLUTION: For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. f(x)= (x+1/5)^4(x-1)^3 Given Answer

Question 893414: For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. f(x)= (x+1/5)^4(x-1)^3
Given Answers are:
a. -1/5, multiplicity 4, touches x-axis;1, multiplicity 3, crosses x-axis
b. 1/5, multiplicity 4, touches x-axis; -1, multiplicity 3, crosses x-axis
c. 1/5, multiplicity 4, crosses x-axis; -1, multiplicity 3, touches x-axis
d. -1/5, multiplicity 4, crosses x-axis; 1, multiplicity 3, touches x-axis

Found 2 solutions by richwmiller, Theo:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
a)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
equation is:

f(x)= (x+1/5)^4 * (x-1)^3

you have 2 roots.

the first root is at x = 1/5 and has a multiplicity of 4 which means that the graph will touch the x-axis at that point but not cross it.

the second root is at x = 1 and has a multiplicity of 3 which means that the graph will cross the x-axis at that point.

here's the graph of your equation.

you solution is selection a.

you can see that the graph touches the x-axis at x = -1/4 and the graph crosses the x-axis at x = 1.

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