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## According to the Rational Root Theorem, which statement about f(x) = 12x^3 – 5x^2 + 6x + 9 is true?

y=12x^3-5x^2+6x+9

Any rational root will be of the form

+-(factor of 9)/(factor of 12)

So we have +-(1,3,9)/(1,2,3,4,6,12) as possibilities.

Think of it this way

Let it be factored as (ax+b)(cx+d)(ex+f)

So a*c*e=12 and b*d*f=9

If this is factored form, (-b/a),(-d/c),(-f/e) will be roots.

This proves that rational roots will be

+-(factor of 9)/(factor of 12)

None of these forms will be a root and therefore the roots of this particular equation are irrational. This can be verified by synthetic division. They are -.6387559, .5277113+-.9464028i

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