Find all possible rational zeros of the equation
Algebra

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Use the rational zeros theorem to list all possible rational zeros of the following
h(x)= 3 + 6x  4x^3 + x^2 + x^4
Be sure that no value in the list appears more than once
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The Rational Zeros Theorem states:
If P(x) is a polynomial with integer coefficients and if is a zero of P(x) ( i.e. P() = 0 ), then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x) .
First arrange the polynomial in descending order.
Constant term is 3.
Its factors are ±1 , ±3.
Coefficient of the leading term is 1
Its factors are ±1.
Possible solutions are .
These can be simplified to ±1 , ±3.
So there are 4 possible solutions which are 1, 1, 3, 3.
Check whether each of them is a zero of h(x) by substituting for x in h(x) such that h(x) = 0.
For x = 1

Please let me know if you need any clarification. I'm always happy to answer your questions.In the same way checking for other values of x i.e. x = 1, x = 3 and x = 3
we get
Hence, h(x) does not have any rational zeros.
Please do ask in case you have any doubts.
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