Rounded to the nearest tenth, find the root of x^3-5x^2-12x+60=0 that lies between 3 and 4. Express your answer as a decimal.
Thanks for the help!
Using the rational root theorem, it's discovered that 5 is a root of the equation.
Thus, x = 5, or x - 5 = 0. This means that x - 5 is a factor of the equation: .
When this equation is divided by the factor, x - 5, its QUOTIENT is: . Thus, the factors of
are: (x - 5) and .
Factoring further, we see that 2 other roots of the equation are: 3.464101615 and - 3.464101615.
Thus, the root that lies between 3 and 4 is: 3.464101615 ≈ (to the nearest tenth).
You can do the check!!
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