Question

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

Answer 1

ANSWER

$x = 0 \: or \: x = \frac{3}{2} \: or \: x = - 3$

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,

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

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

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

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

$x = 0 \: or \: x = \frac{3}{2} \: or \: x = - 3$

Answer 2

Answer:

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

Step-by-step 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