Question

What are the zeros of the function `f(x)= 3x^2-3x-6`?

Answer 1

`x=-1` and `x=2`

Explanation:

Step 1. Factor out the function you were given

`f(x)=3x^2-3x-6`
`" "=3(x^2-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]()

Answer 2

`x=-1,x=2`

Explanation:

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

`"solve "3x^2-3x-6=0`

`rArr3(x^2-x-2)=0larr" common factor of 3"`

`rArr3(x-2)(x+1)=0larr" factorise quadratic"`

`x-2=0rArrx=2larr" is a zero"`

`x+1=0rArrx=-1larr" is a zero"`