Find the Roots (Zeros) f(x)=3x^3-12x^2-15x

Problem

ƒ(x)=3*x3−12*x2−15*x

Solution

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

3*x3−12*x2−15*x=0

2. Factor out the greatest common factor, which is 3*x

3*x*(x2−4*x−5)=0

3. Factor the quadratic expression inside the parentheses by finding two numbers that multiply to −5 and add to −4

3*x*(x−5)*(x+1)=0

4. Apply the Zero Product Property by setting each individual factor equal to zero.

3*x=0

x−5=0

x+1=0

5. Solve for x in each equation to determine the roots.

x=0

x=5

x=−1

Final Answer

x={0,5,−1}

Want more problems? Check here!