Find the x-intercepts (if any)of the graph of the function. If the x-intercepts are irrational, round your answers to the
nearest tenth.
-$$f ( x ) = x ^ { 2 } - 5 x + 1$$
A)No x-intercepts
B)x-intercepts: (-1, 0)and (5, 0)
C) $$\mathrm { x } \text {-intercepts: } ( 0.2,0 ) \text { and } ( 4.8,0 )$$
D) $$\text { x-intercepts: } \left( \frac { - 5 \pm 4.6 } { 2 } , 0 \right)$$

Question

Quizplus · Accepted Answer

To find the x-intercepts, we set $f(x) = 0$ and solve for $x$. Thus, $x^2 - 5x + 1 = 0$. This is a quadratic equation, and we can use the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ with $a = 1$, $b = -5$, and $c = 1$. Plugging these values in gives $x = \frac{5 \pm \sqrt{(-5)^2 - 4(1)(1)}}{2(1)} = \frac{5 \pm \sqrt{25 - 4}}{2} = \frac{5 \pm \sqrt{21}}{2}$. Since $\sqrt{21}$ is approximately 4.58, the solutions are approximately $x = \frac{5 \pm 4.58}{2}$, which gives the approximate solutions $x \approx 0.2$ and $x \approx 4.8$, rounded to the nearest tenth.

Find the X-Intercepts (If Any)of the Graph of the Function f(x)=x2−5x+1f ( x ) = x ^ { 2 } - 5 x + 1f(x)=x2−5x+1

Find the X-Intercepts (If Any)of the Graph of the Function $f ( x ) = x ^ { 2 } - 5 x + 1$