Find the Roots (Zeros) 5x^3-2x^2-10x+4=0

Problem

5*x^3−2*x^2−10*x+4=0

Solution

1. Group the terms to prepare for factoring by grouping.

(5*x^3−2*x^2)+(−10*x+4)=0

2. Factor out the greatest common factor from each group.

x^2*(5*x−2)−2*(5*x−2)=0

3. Factor out the common binomial (5*x−2) from the expression.

(5*x−2)*(x^2−2)=0

4. Set each factor to zero using the zero product property.

5*x−2=0

x^2−2=0

5. Solve for x in the first linear equation.

5*x=2

x=2/5

6. Solve for x in the second quadratic equation by taking the square root of both sides.

x^2=2

x=±√(,2)

Final Answer

x=2/5,√(,2),−√(,2)

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