list all possible positive real zeros and the number of possible negative real zeros. Determine all the rational zeros to 2x^4 - x^3 - 6x + 3

Guest Oct 17, 2014

#2**+10 **

All the possible rational real zeroes are given by all the factors of p divided by all the factors of q where p is 3 and q is 2.

So we have ±3 ±1 ±3/2 ±1 ±1/2

And, as Alan found, the only rational real is 1/2.

Notice that the Rational Zeroes Theorem doesn't * guarantee* any real rational roots. It just says that, if there are any, they will come from the p/q list.

CPhill
Oct 17, 2014

#1**+5 **

This can be factored as (2x - 1)(x^{3} - 3) so there is a zero at the positive rational value 1/2 and at the positive irrational value ^{3}√3. The other two roots are complex. There are no negative real roots.

.

Alan
Oct 17, 2014

#2**+10 **

Best Answer

All the possible rational real zeroes are given by all the factors of p divided by all the factors of q where p is 3 and q is 2.

So we have ±3 ±1 ±3/2 ±1 ±1/2

And, as Alan found, the only rational real is 1/2.

Notice that the Rational Zeroes Theorem doesn't * guarantee* any real rational roots. It just says that, if there are any, they will come from the p/q list.

CPhill
Oct 17, 2014