For the polynomial, list each real zero and its multiplicity. Determine whether

Question

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(x2 - 5)

1.    (sqrt{5}, multiplicity 1, touches x-axis; -sqrt{5}, multiplicity 1, touches x-axis)   

2. 0, multiplicity 1

3. 0, multiplicity 1, touches x-axis;    (sqrt{5}, multiplicity 1, touches x-axis; -sqrt{5}, multiplicity 1, touches x-axis)   

4. 0, multiplicity 1, crosses x-axis;    (sqrt{5}, multiplicity 1, crosses x-axis; -sqrt{5}, multiplicity 1, crosses x-axis)   

Explanation / Answer

f(x) =x(x^2-5)

x =0 multiplicity of 1, crosses the x axis

x^2=5

x = sqrt 5 multiplicity of 1, crosses the x axis

x = -sqrt 5 multiplicity of 1, crosses the x axis

therefore answer is 4

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