Question
Use rational root theorem and the factor theorem to help solve the following equation
X4-2x3-13x2+38x-24=0
X4-2x3-13x2+38x-24=0
Answers
Steve
If there rational roots to
x^4 - 2x^3 - 13x^2 + 38x - 24 = 0
then the numerator must divide 24 and the denominator must divide 1.
In other words, the roots must be a factor of 24, in this case.
The factor theorem says that if x-a divides f(x), then a is a root of f(x) = 0.
A little easy synthetic division reveals that roots are present at
x = 1,2,3,-4
x^4 - 2x^3 - 13x^2 + 38x - 24 = 0
then the numerator must divide 24 and the denominator must divide 1.
In other words, the roots must be a factor of 24, in this case.
The factor theorem says that if x-a divides f(x), then a is a root of f(x) = 0.
A little easy synthetic division reveals that roots are present at
x = 1,2,3,-4