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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

Best Answer 

 #2
avatar+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
avatar+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
avatar+98196 
+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

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