Question

What are the zeros of f(x)=2x^3+3x^2-9x?

Answer 1

x = -3, x= 0, and x = 1.5

Explanation:

The zeros of a function f(x) refers to the x-values for which f(x) = 0.

We simply graph the function and determine the points where the graph crosses the x-axis. Thus, we shall be solving the problem graphically;

From the attachment below, the graph of f(x) crosses the x-axis at;

x = -3, x= 0, and x = 1.5

Answer 2

`x = 0 \: or \: x = (3)/(2) \: or \: x = - 3`

EXPLANATION

The given polynomial function is

`f(x) =2{x}^(3) + 3 {x}^(2) - 9x`

To find the zeros, we equate the function to zero.

`2{x}^(3) + 3 {x}^(2) - 9x = 0`

Factor x,

`x(2 {x}^(2) + 3x - 9) = 0`

Split the middle term,

`x(2 {x}^(2) + 6x - 3x - 9) = 0`

`x(2x(x + 3) - 3(x + 3) = 0`

`x(2x - 3)(x + 3) = 0`

`x=0,2x-3=0,x+3=0`

`x = 0 \: or \: x = (3)/(2) \: or \: x = - 3`