# Use the rationals theorem

posted by .

Use the rationals theorem to find all the zeros of the polynomial function. Use the zeros to factor f over the real numbers.
f(x)=2x^3-x^2+2x-1

• Use the rationals theorem -

follow the same steps I just showed you in your last post
http://www.jiskha.com/display.cgi?id=1364332046

• Use the rationals theorem -

I like this variant which makes use of candidates that turn out not to be a zero. This works as follows.

The possible zeroes are:

x = -1,1,1/2,-1/2 (1)

We have:

f(1) = -2

If we put

g(t) = f(1+t)

then the coefficient of t^3 is 2 and the constant term is f(1) = -2, the possible zeroes are thus:

t = +/-1 , +/-2, +/- 1/2

The possible zeroes of f are thus:

x = 1+t = 0,2,-1,3,1/2,3/2

But since all the possible zeroes are listed in (1), we can strike out the elements that are not on that list. We are thus left with:

x = -1,1/2

Then since -1 is not a zero, the only possible rational zero is 1/2, which is indeed a zero. Then you can proceed by dividing f(x) by x-1/2 and find the zeroes of the quadratic.

## Similar Questions

1. ### college algebra

use rational zeros theorem to find all the real zeros in the polynomial function. use zeros to factor f over real numbers. f(x)=x^3+10x^2-13x-22 find real zeros of f?
2. ### college algebra

use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x)=x^3-8x^2-31x-22
3. ### calculus

use rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x)=x^3-8x^2-31x-22 **please show work**
4. ### College algebra

Use the rationals theorem to find all the zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x)=x^3-2x^2-13x-10 x=
5. ### College Algebra

Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x)=2x^3-x^2+2x-1
6. ### College algebra

Use the rationals theorem to find all the zeros of the polynomial function. Use the zeros to factor f over the real numbers, F(x)=7x^3-x^2+7x-1
7. ### rational zeros theorem

Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x)=25x^4+26x^3+126x^2+130x+5 Find the real zeros x= Use the real zeros to factor f f(x)=
8. ### pre calculus

use the rational zeros theorem to find all the real zeros of the polynomial function. use the zeros to factor f over the real numbers: f(x)=x^4+2x^3-7x^2-8x+12 I am totally lost, please help?
9. ### College algebra

Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers f(x)=9x^4+28x^3+66x^2+196x+21 Find the real zeros of f Use the real zeros to factor f f(x)=
10. ### algebra

Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x)= x^4+6x^3-11x^2-24x+28 Molon

More Similar Questions