Question

What is the rational zeros theorem?

Answer 1

The rational zeros theorem (also called the rational root theorem) is used to check whether a polynomial has rational roots (zeros).

Answer 2

How does it work?

Answer 3

It gives a list of possible rational zeros of a polynomial function.

Answer 4

f(x) = -2x^4 + 4x^3 + 3x^2 + 18 i am supposed to use it with this to find all the rational zeros

Answer 5

@wmckinely please help

Answer 6

@rajee_sam can you help me again please

Answer 7

Ok rational root theorem gives you all the possibilities of rational roots for a given polynomial.

I look at the polynomial and determine the coefficient of the leading term and the constant term. In the given function the leading coefficient is -2 ( Because the degree of the polynomial is 4 because x^4 is the highest exponent of x.) The constant term is 18.

Now I list all the possible factors of -2 and 18.

Possible factors of -2 are \[\pm2, \pm1\]

Answer 8

The possible factors of 18 are, \[\pm1, \pm2, \pm3, \pm6, \pm9, \pm18\]

Answer 9

Now the possible roots are obtained by dividing the roots of the constant term by the roots of the leading coefficient.

the possible roots will be \[\pm 1/ \pm 2 = \pm 1/2; \pm 2/ \pm 2 = \pm 1; \pm 3 / \pm 2 = \pm 3/2; \pm 6 / \pm 2 = \pm 3; \]\[\pm 9 / \pm 2 = \pm 9/2; \pm 18 / \pm 2 = \pm 9;\]\[\pm 1 / \pm 1 = \pm 1; \pm 2 / \pm 1 = \pm 2; \pm 3 / \pm 1 = \pm 3; \pm 6/ \pm 1 = \pm 6; \pm 9/ \pm 1 = \pm 9\] \[\pm 18 / \pm 1 = \pm 18;\]

Now if you consolidate all the roots the following are the possible rational roots for the given polynomial.

\[\pm 1/2 \space ; \space \pm 1\space ; \space \pm 3/2 \space ; \space \pm 2 \space ; \space \pm 3 \space ; \space \pm 6 \space ; \space \pm 9/2 \space ; \space \pm 9 \]

Answer 10

also \[\pm 18\]

Answer 11

forgot that