How to do this question?
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"How does Bohr improve Rutherford's atomic model?"
Rational root theorem states that rational roots of a polynomial will take the form of #p/q# where #p# is a factor of the constant term and #q# is a factor of the leading coefficient. So, for #f(x)=12x^3+20x^2-x-6#
#p={1,2,3,6}#
#q={1,2,3,4,6,12}#
#p/q={+-1,+-1/2,+-1/3,+-1/4,+-1/6,+-1/12,+-2,+-2/3,+-3,+-3/2,+-3/4,+-6}# (take each value of p and divide it by each and every value of q)
Now, theoretically, we would test each of these #p/q# values to find which ones are actually zeros of the function #f(x)=12x^3+20x^2-x-6#
Truthfully, what you can do is find the rational zeros in your calculator and prove that they are zeros by using traditional or synthetic substitution. Once you know a root, the factor is #(x-a)# where #a# is your root.
