Question 466180: find all of the zeros and state any multiplicity for
j(x)=-2x^3 + 6x^2 - 9/2x
k(x)=x^3 - 28x -48
m(x)= x^4 - x^2 - 20
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! find all of the zeros and state any multiplicity for
j(x)=-2x^3 + 6x^2 - 9/2x
k(x)=x^3 - 28x -48
m(x)= x^4 - x^2 - 20
...
j(x)=-2x^3+6x^2-9/2x=0
factor out 2x
2x(x^2+3x+9/4)=0
2x(x+3/2)^2=0
2x=0
x=0
or
x=-3/2 (multiplicity 2)
zeros: 0, -3/2 , -3/2
..
k(x)=x^3-28x-48=0
x=-2 (from graphing calculator)
By long division or synthetic division
(x^3-28x-48)/(x+2)=x^2-2x-24=(x-6)(x+4)
zeros: -4, -2, 6
..
m(x)= x^4-x^2-20=0
(x^2-5)(x^2+4)=0
x^2-5=0
x^2=5
x=±√5
..
x^2+4=0
x^2=-4
x=±2 i (2 imaginary roots)
zeros: -√5, √5 and 2 imaginary roots
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