Find the zeros of the function: f(x) = 3x3 - 12x2 - 15x

Question

johnweldon1993 · Answer

what can be factored out of each of the terms?

johnweldon1993 · Answer

also notice that there IS at least 1 "x" in each term.....so you can factor out an x as well

anonymous · Answer

First use the factor theorem, by which we know that the factors of -15 divided by the factors of 3 are potential 0s. List all these out and try some. As soon as you find one that results in f(x) = 0, you know that the value is a 0. 

For example, if 1/2 is a potential zero of an arbitrary third degree function and by inserting x = 1/2  f(x) = 0, then 2x - 1 is a zero. Dividing the expression by 2x - 1 using long division will then result in a quadratic which you can normally factor and get all the zeroes. 

Try doing this to find the the zeros of this third degree polynomial.

@nadc2005

anonymous · Answer

$$3x ^{3}-12x ^{2}-15x = 0$$
Factor the left side,
$$3(x-5)x(x+1)=0$$
$$(x-5)x(x+1)=0$$
We take the 3 to the other side and divide it by 0, which gives us 0.
Then equate each part to 0 individually,
$$x=0$$
$$x-5 = 0; x = 5$$
$$x+1 = 0; x=-1$$

So the zeroes are 0, 5, and -1.