Question

How many x-intercepts appear on the graph of this polynomial function?

1 Rx)= x -x + x²-x
1 x-intercept
2 x-intercepts
3 x-intercepts
4 x-intercepts

Answer 1

2 x-intercepts on edge2020

Explanation:

Answer 2

The given function
`R(x) = x - x + x^2  - x` has 2 x -intercepts.

Explanation:

Here, the given polynomial function is :

`R(x) = x - x + x^2  - x\\\implies R(x) = x^2 - x`

or,
`y  = x^2 - x` ............ (1)

X- intercept is the point in the graph of R(x), where the coordinate y = 0.

Now, substituting the value of y = 0 in (1) find all x - intercepts:

`y  =  0   \implies x^2 - x = 0\\x(x-1)  =0\\\implies(x-0)(x-1) = 0`

⇒ Either x = 0 , or x - 1 = 0 ⇒ x = 1

⇒The given function has two x intercepts at x = 0 and x = +1

Hence, the given function
`R(x) = x - x + x^2  - x` has 2 x -intercepts.