+0

help with rational root thm.

0
456
2

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

Oct 17, 2014

#2
+98196
+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.

Oct 17, 2014

#1
+27566
+5

This can be factored as (2x - 1)(x3 - 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.

.

Oct 17, 2014
#2
+98196
+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