Using complete sentences, explain how to find the zeros of the function f(x) = 2x^3 – 9x + 3

To find the zeros of the function f(x) = 2x^3 - 9x + 3, we
need to equate f(x) to 0 and solve the equation we
get.

Here we have to solve 2x^3 - 9x + 3 =
0

As the highest power of x among all the the terms is 3,
we will get 3 values for x which satisfy the equation.

The
function has 3 zeros.

To find the roots of the cubic
equation that we have got, the following formula can be
used

2x^3 - 9x + 3 =
0

=> x^3 - (9/2)x + 3/2 =
0

a = -9/2 and b = 3/2

Now
substitute the values of a and b in the following to determine the three
zeros:

Let A =
cuberoot(-b/2+sqrt(b^2/4+a^3/27))

and B =
cuberoot(-b/2-sqrt(b^2/4+a^3/27))

Then the three solutions
are:

x1 = A +
B

x2 = -(A+B)/2 +
(A-B)sqrt(-3)/2

and x3=
-(A+B)/2 - (A-B)sqrt(-3)/2