What are the zeros of the function f(x)=3x2−3x−6?

2 Answers
Andy Y.
Feb 9, 2017

x=−1 and x=2

Explanation:

Step 1. Factor out the function you were given

f(x)=3x2−3x−6
=3(x2−x−2) ...factor out 3, common to all three terms
=3(x+1)(x−2) ...identify a factorization of the polynomial

Step 2. Set the factored function equal to zero and solve

3(x+1)(x−2)=0

  • 3 is not zero
  • (x+1)=0 when x=−1
  • (x−2)=0 when x=2

Step 3. Verify these roots are zeros of the function by graphing

![Socratic.org graph, modified by MS Paint](useruploads.socratic.org)

Jim G.
Feb 9, 2017

x=−1,x=2

Explanation:

The zeros of f(x) are the values of x which make f(x) = 0

solve 3x2−3x−6=0

⇒3(x2−x−2)=0← common factor of 3

⇒3(x−2)(x+1)=0← factorise quadratic

x−2=0⇒x=2← is a zero

x+1=0⇒x=−1← is a zero

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