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
+128474 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.
+33615 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.
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+128474 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.
