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

1 Answer
Oct 28, 2015

Answer:

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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