How do you use the rational root theorem to find the roots of x^4 – 7x^2 + 12 = 0?

1 Answer
Oct 28, 2015

Evaluation of x^4-x^2+12 for all factors of 12
gives the roots x=2 and x=-2

Explanation:

According to the Rational Root Theorem in its simplified form
when f(x)is a monic polynomial (a polynomial whose highest degree term has a coefficient of 1)
if a is a rational root of f(x) then a must be a factor of the constant term of f(x)

For the given example, this means that any rational root of x^4-7x^2+12 but be a factor of 12.

The factors of 12 are {1,2,3,4,6,-1,-2,-3,-4,-6}

We can test each of these factors (as I did with Excel, below) to find all rational roots of f(x)
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