To find the zeros of a function, you have to solve
[tex] f(x) = 0 \implies 3x^2-12x-36=0 [/tex]
Note that you can factor a 3 out of your equation, which simplifies the computations a little bit:
[tex] 3x^2-12x-36 = 3(x^2-4x-12)=0 \iff x^2-4x-12=0 [/tex]
In cases like this (i.e. when the coefficient of x^2 is 1) you can use an alternative formula which can save some time: the two solutions are two numbers such that:
- Their sum is the opposite of the x coefficient
- Their product is the constant term.
In our case, the x coefficient is -4, so we're looking for two numbers that give 4 when summed. Also, the constant term is -12, so we're looking for two numbers that give -12 when multiplied.
A bit of easy trial and error will lead to the answer
[tex] x_1 = -2,\quad x_2 = 6 [/tex]
