Find the Roots (Zeros) f(x)=6x^2+6x-36

Problem

ƒ(x)=6*x2+6*x−36

Solution

1. Set the function to zero to find the roots of the quadratic equation.

6*x2+6*x−36=0

2. Factor out the greatest common factor which is 6 to simplify the equation.

6*(x2+x−6)=0

3. Divide both sides by 6 to isolate the quadratic trinomial.

x2+x−6=0

4. Factor the trinomial by finding two numbers that multiply to −6 and add to 1 These numbers are 3 and −2

(x+3)*(x−2)=0

5. Apply the Zero Product Property by setting each linear factor equal to zero.

x+3=0

x−2=0

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

x=−3

x=2

Final Answer

x=−3,2

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