Question 715742: Use the rational root theorem to list all possible rational roots for each equation.then find any actual roots.
1). X^4-7x^2+12=0
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Rational roots would be fractions (negative and positive)
whose numerator is a factor of the independent term, the constant  ,
and whose denominator is a factor of the leading coefficient, the invisible  in front of  .
The denominator can only be , the only factor of ,
but has 6 factors:
1, 2, 3, 4, 6, and 12.
So the possible rational roots are:
-12, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6, and 12.
Finding the roots is easier.
No need to try any of those rational roots.
If we change variables using  ,
the equation becomes
 -->  and that factoring tells us that
 and  are solutions of
and will lead us to solutions of 
 leads us to  and  (not rational roots< but at least real roots)
 leads us to
 -->  and
 -->  (two of the 12 possible rational roots).
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