Question 41950: find any rational roots for the equation x^3+x^2-4x+4=o
Answer by mbarugel(146)   (Show Source):
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A possible way to solve this is through the Rational Roots Test (RRT) and by graphing.
According to the RRT, if there are any rational roots, they will be of the form:
(plus-or-minus)(factor of the constant term)/(factor of the leading coefficient)
The constant term is 4, so its factors are 1, 2 and 4. The leading coefficient term is 1 (because the value multiplying x^3 is 1). Therefore, the possible rational roots would be:
-1, 1, -2, 2, -4, 4
Let's draw a graph of x^3+x^2-4x+4 to see if there are any roots that come close to these values:
As you can see, none of the roots is near the possible values for rational root, so we conclude that there are NO RATIONAL ROOTS. Indeed, the only real root is an irrational number: -2.8751297...
I hope this helps!
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