Answer
The equation has no $x$-intercept
Work Step by Step
$y=x^{2}-5x+8$
To find the $x$-intercepts of this equation, set $y$ equal to $0$ and solve for $x$:
$x^{2}-5x+8=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
In this case, $a=1$, $b=-5$ and $c=8$
Substitute the known values into the formula and evaluate:
$x=\dfrac{-(-5)\pm\sqrt{(-5)^{2}-4(1)(8)}}{2(1)}=\dfrac{5\pm\sqrt{25-32}}{2}=...$
$...=\dfrac{5\pm\sqrt{-7}}{2}=\dfrac{5}{2}\pm\dfrac{\sqrt{7}}{2}i$
Since the solutions of the equation are complex numbers, the original equation has no $x$-intercepts.
