Answer: 2
Step-by-step explanation:
x⁴ - x³ + x² - x
Factor to find the zeros:
x³(x - 1) + x(x - 1)
= (x³ + x)(x - 1)
= x(x² + 1)(x - 1)
Zeros are: x = 0, x = ±i, x = 1
There are two real zeros and two imaginary zeros.
The x-intercepts are the two real zeros: at x = 0 and x = 1
X-intercepts on the graph of the polynomial function
[tex]f(x) = x^{4} -x^{3} +x^{2} -x[/tex] is 2 x-intercept.
" X- intercept is defined as the when line passes through x- axis at y = 0."
According to the question,
Given polynomial function,
[tex]f(x) = x^{4} -x^{3} +x^{2} -x[/tex]
To get x- intercept polynomial function f(x) =0 we get,
[tex]x^{4} -x^{3} +x^{2} -x = 0[/tex]
⇒[tex]x^{3} (x-1)+ x(x-1)=0[/tex]
⇒[tex](x^{3} +x)(x-1)=0[/tex]
⇒ [tex]x(x^{2} +1)(x-1)=0[/tex]
⇒ [tex]x=0 , x=1 , x=\sqrt{-1}[/tex]
Here , two possible real values are there for x-intercept x=0 and x=1.
Hence, X-intercepts on the graph of the polynomial function
[tex]f(x) = x^{4} -x^{3} +x^{2} -x[/tex] is 2 x-intercept.
Learn more about x-intercept here
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