Question 976976
f(x) = x^4 − x^3 − 20x^2 
What are all the zeros of the function and determine the multiplicity of each zero and the number of turning points of the graph of the function.
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f(x) = x^4 − x^3 − 20x^2 
f(x) = x^2(x^2 − x − 20)
x^2(x^2 − x − 20)=0
x^2(x-5)(x+4)=0
zeros are: 0, -4, 5
multiplicity=1 for all zeros
number of turning points=3
see graph below:

{{{ graph( 300, 300, -8, 8, -150,30, (x^4-x^3-20x^2) ) }}}