SOLUTION: Use the Rational Zero theorem. First find the potential zeros from the factors of p and the factors of q, then test then by the synthetic division or the polynomial division. Sec

Question 468916: Use the Rational Zero theorem. First find the potential zeros from the factors of p and the factors of q, then test then by the synthetic division or the polynomial division.
Section 4.5 #60 In Problems 57�68, solve each equation in the real number system 2x3 � 3x2 � 3x � 5 = 0
Can someone please help me with this problem? thank you. I answered it on my on and I got it wrong.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Use the Rational Zero theorem. First find the potential zeros from the factors of p and the factors of q, then test then by the synthetic division or the polynomial division.
Solve each equation in the real number system 2x3 � 3x2 � 3x � 5 = 0 .
...
factors of p=5: �1, �5
factors of q=2: �1, �2
possible rational roots(p/q):�1, �1/2, �5/2
Finding real number roots using synthetic division:
0).......2...-3...-3...-5
1).......2...-1...-4...-5
1/2)...2...-2...-4...-3
5/2)...2.....2.....2... 0 (root)
P(x)=(x-5/2)(2x^2+2x+2)
2x^2+2x+2=0
x^2+x+1=0
x=[-1�sqrt(1-4*1*1)]/2*1
x=(-1�√-3)/2
Given function has one real root,x=5/2, and two imaginary roots, x=(-1�√-3)/2
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