SOLUTION: P(x) = 3x^3 + x2 − 7x − 5 What are all possible rational zeros of P given by the Rational Zeros Theorem?
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Question 947522: P(x) = 3x^3 + x2 − 7x − 5 What are all possible rational zeros of P given by the Rational Zeros Theorem?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the rational roots are all the possible factors of p divided by q after you have reduced that fraction to simplest terms.
p is the constant term.
q is the leading coefficient.
your p is equal to 5
your q is equal to 3
the possible factors of 5 are 1,5
the possible factors of q are 1,3
the possible factors of p/q are 1/1, 1/3, 5/1, 5/3.
the possible rational roots are plus or minus the possible factors of p/q.
as it turns out, the roots are x = -1 and x = 5/3.
a graph of the equation is shown below:
1.667 shown on the graph is equal to 1 and 2/3 which is equal to 5/3.
the solution of x = -1 is actually encountered twice, so the factors of the equation are:
(x+1) * (x+1) * (x-5/3) = 0
if you multiply those factors out, you will get back to the original equation.
so you have 3 rational roots to the equation.
-1 is encountered twice and 5/3 is encountered once.
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