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

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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

Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial