Find all possible rational zeros of the equation

Algebra
Tutor: None Selected Time limit: 1 Day

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

Oct 16th, 2015

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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

 


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Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 16th, 2015

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.


Oct 16th, 2015

Please do ask in case you have any doubts.

Oct 16th, 2015

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