SOLUTION: List the possible solutions:
{{{P(x)=-3x^5-x^3-4x^4-5}}}
I tried grouping but that was a dead end and I don't know what else to do with this because it has 4 terms. Could you ple
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Question 1129875: List the possible solutions:
I tried grouping but that was a dead end and I don't know what else to do with this because it has 4 terms. Could you please help?
Found 2 solutions by rothauserc, MathLover1:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Use The Rational Zeros Theorem since all the coefficients are integers
:
-3x^5 -x^3 -4x^4 -5 = 0
:
possible solutions or zeros are where f(x) crosses the x-axis
:
since the max degree of the given polynomial is 5, we expect to have 5 solutions
:
every rational zero of the given polynomial has the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient
:
constant term is -5 and the leading coefficient is -3
:
the factors of p are +or-1, +or-5
:
the factors of q are +or-1, +or-3
:
we have +or-1/1, +or-1/3, +or-5/1, +or-5/3
:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Use the Rational Roots Test to Find All Possible Roots:
find every combination of ± where is a factor of the constant and is a factor of the leading coefficient
The constant term of this polynomial is , with factors and .
The leading coefficient is , with factors and.
Tests yields the following possible solutions:
±, ±, , ± , ±
test them:
-> does not work
-> does not work
-> does not work
-> does not work
-> does not work
-> does not work
-> does not work
-> does not work
This polynomial has no rational roots that can be found using Rational Root Test.
try to find roots using Newton method:
If is an approximation a solution of and if ′
the next approximation is given by, /′
'
≈
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