Find the Roots (Zeros) F(x)=2x^3-4x^2-10x+20

Problem

F(x)=2*x3−4*x2−10*x+20

Solution

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

2*x3−4*x2−10*x+20=0

2. Factor by grouping by splitting the terms into two pairs.

(2*x3−4*x2)+(−10*x+20)=0

3. Factor out the greatest common factor from each pair.

2*x2*(x−2)−10*(x−2)=0

4. Factor out the common binomial (x−2) from the expression.

(2*x2−10)*(x−2)=0

5. Set each factor to zero to solve for x

2*x2−10=0

x−2=0

6. Solve the linear equation for the first root.

x=2

7. Solve the quadratic equation for the remaining roots by isolating x2

2*x2=10

x2=5

x=±√(,5)

Final Answer

x=2,√(,5),−√(,5)

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