Question

Which of the following plotted points on the graph represent the zeros of the function g(x)= (x^2-3x-10) (x+4)?

(-2,0)
(4,0)
(0,10)
(-4,0)
(0,-2)
(0,-10)
(5,0)

Answer 1

(x^2-3x-10)(x+4) factor first parenthetical term

(x^2+2x-5x-10)(x+4)

(x(x+2)-5(x+2))(x+4)

(x-5)(x+2)(x+4), so the zeros occur when x={-2,-4,5} which are the points:

(-2,0),(-4,0), and (5,0)

Answer 2

Answer: The correct points are (-2, 0), (-4, 0) and (5, 0).

Step-by-step explanation: The given function is

`g(x)=(x^2-3x-10)(x+4).`

We are given to select the correct points from the options that will represent the zeroes of the function g(x).

The points at which the values of 'x' results in zero value of g(x) are called the zeroes of the function g(x).

Since g(x) is a cubic function, so it will have three zeroes.

The given function is

`g(x)\\\\=(x^2-3x-10)(x+4)\\\\=(x^2-5x+2x-10)(x+4)\\\\=\{x(x-5)+2(x-5)\}(x+4)\\\\=(x+2)(x-5)(x+4).`

We have

if x = -2, then g(x) = 0,

if x = -4, then g(x) = 0,

if x = 5, then g(x) = 0.

g(x) will not be zero for any other value.

Thus, the points representing zeroes of g(x) are (-2, 0), (-4, 0) and (5, 0).