SOLUTION: plz help me with this maths equation i will be really thankful
Q) which of the following sets are equal?
A={1,2,3}
B={x:x^2-2*x+1=0}
and C={x:x^3-6*x^2+11*x-6=0}
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Question 906574: plz help me with this maths equation i will be really thankful
Q) which of the following sets are equal?
A={1,2,3}
B={x:x^2-2*x+1=0}
and C={x:x^3-6*x^2+11*x-6=0}
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
as far as i can see, none of them are equal.
A is the set {1,2,3}
there are 3 elements in the set.
those elements are x = 1, x = 2, x = 3.
B is solved for as follows:
x^2 - 2x + 1 = 0
factor this to get (x-1)^2 = 0
that gets you x = 1 as the only value of x in the set.
C is solved for as follows:
start with x^3 - 6x^2 + 11x - 6 = 0
your rational roots, if any, will be a combination of the factors of the coefficient of x^3 multiplied by the factors of the constant term.
that would make the possible roots as plus or minus {6,3,2,1)
you can use synthetic division to eliminate these possibilities.
6 is not a root, but 1, 2, and 3 are all roots.
selections A and C are equivalent.
if you need help on how to perform synthetic division, here's a reference.
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut37_syndiv.htm
if you need help on how to determine the rational roots of an equation, here's a reference that can help.
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut38_zero1.htm
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