SOLUTION: Hey ! I need help solving this. 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 tur

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hey ! I need help solving this. 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 tur      Log On


   

Question 976976: Hey ! I need help solving this.
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.
Thank you!
Found 2 solutions by MathLover1, lwsshak3:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+x%5E4+-x%5E3+-+20x%5E2+
set f%28x%29+=0
0=+x%5E4+-x%5E3+-+20x%5E2+....factor out x%5E2
0=+%28x%5E2+-+x+-+20%29x%5E2+....factor completely %28x%5E2+-+x+-+20%29+, replace -x with 4x-5x
0=+%28x%5E2+-+4x%2B5x+-+20%29x%5E2+......group
0=+%28%28x%5E2+-+4x%29%2B%285x+-+20%29%29x%5E2+
0=+%28x%28x+-+4%29%2B5%28x+-+4%29%29x%5E2+
0=+%28x%2B4%29%28x-5%29x%5E2+
so, zeros are:
0=+%28x%2B4%29+=>x=-4-the multiplicity 1
0=+%28x-5%29+=>x=5-the multiplicity 1
0=+x%5E2+=>x=0, -the multiplicity 2

+graph%28+600%2C+600%2C+-20%2C+20%2C+-150%2C+90%2C++%28x%2B4%29%28x-5%29x%5E2%29+
as you can see, there are 3 turning points of the graph of the function

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
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.
***
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%28+300%2C+300%2C+-8%2C+8%2C+-150%2C30%2C+%28x%5E4-x%5E3-20x%5E2%29+%29+