Factoring a polynomial
We know that a function intercepts x-axis when y = 0.
For the following function:
[tex]\begin{gathered} f(x)=x^2-2x+5 \\ y=x^2-2x+5 \end{gathered}[/tex]
we want to know which values should have x so y = 0, then
[tex]\begin{gathered} y=x^2-2x+5 \\ 0=x^2-2x+5 \end{gathered}[/tex]
We rearrange the function so it can be expressed in the perfect square polynomial form:
x² - 2x + 5 = 0
x² + 2(- 1x) = -5
x² + 2(- 1x) + 1 = -5 + 1
x² + 2(- 1x) + 1 = - 4
(x - 1) ² = -4
We know must clear x from the equation:
(x - 1) ² = -4
x - 1 = √ (-4)
x - 1 = √ (-4) + 1
Since
√ (-4) doesn't exist because -4 is a negative number, then, this function has no intercepts with x-axis
Answer: A
