Find the solution of the equation: x^3−3x^2+2x−2=0 Approximate your answer to the nearest hundredth.

Question

Find the solution. 

Answer 1

Simplify or factor terms with X:

 

(X^2 - 3X + 2)*X - 2 = 0

 

Then further simplify or factor:

 

(X - 2)*(X - 1)*X - 2 = 0

 

Therefore, you can find the first two "easy" roots, X = 2  and X = 1

 

But you need the 3rd root to show where the function crosses the abscissa (X-axis) at Y = 0

 

You can either plot function or solve by a Newton-Raphson method or use trial-n-error guessing - keep inserting a value for X until you reach a solution at a couple places past the decimal point .. the latter method is time-consuming

 

I obtained X = 2.5214   (to nearest 10,000th)

 

where: f(X) = 0.0001206203     so this should be adequate