Find the Roots (Zeros) f(x)=2x^3-4x^2-22x+44

Problem

ƒ(x)=2*x3−4*x2−22*x+44

Solution

1. Set the function to zero to find the roots of the polynomial.

2*x3−4*x2−22*x+44=0

2. Factor out the greatest common factor from the entire expression to simplify the equation.

2*(x3−2*x2−11*x+22)=0

3. Apply factoring by grouping to the terms inside the parentheses.

2*((x3−2*x2)−(11*x−22))=0

4. Factor out common terms from each group.

2*(x2*(x−2)−11*(x−2))=0

5. Factor out the common binomial (x−2)

2*(x2−11)*(x−2)=0

6. Set each factor to zero using the Zero Product Property.

x−2=0

x2−11=0

7. Solve for x in each resulting equation.

x=2

x2=11

x=±√(,11)

Final Answer

x=2,√(,11),−√(,11)

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