Question 87746
i have never used this rational zeros theorem - i have had a quick look on the web and i think i understand, so here goes.

q is the factors of 1 --> the coefficient of the x^4 term
p is the factors of 12


q = +1, -1
p = 1,2,3,4,6,12,-1,-2,-3,-4,-6,-12


Now, N=p/q gives all RATIONAL values that when put into the polynomial and give zero are solutions. For our values of p and q, we get N=1,2,3,4,6,12,-1,-2,-3,-4,-6,-12 as possible solutions to the polynomial.


However, putting each of these as x into the polynomial - none gives us zero when we raise it to the power 4 and then subtract 12.


So, the conclusion is that if there is a real solution, it has to be irrational. Thinking about this particular case, we have {{{ x^4=12 }}} and so there is a real solution...there is a number that multiplies by itself 4 times to give 12 and it is between 1 and 2 since {{{1^4 = 1}}} and {{{2^4=16}}}.


cheers
Jon.