Answer:
x = 3, x = 1
The points at which the curve crosses the x-axis are (3, 0) and (1, 0)
Step-by-step explanation:
Quadratic formula:
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
Quadratic equation: [tex]ax^2+bx+c[/tex]
Therefore, for [tex]x^2-4x+3[/tex]:
a = 1 b = -4 c = 3
Inputting values into quadratic formula:
[tex]x=\dfrac{4\pm\sqrt{(-4)^2-(4\times1\times3)} }{2\times1}[/tex]
[tex]\implies x=\dfrac{4\pm\sqrt{16-12} }{2}[/tex]
[tex]\implies x=\dfrac{4\pm\sqrt{4} }{2}[/tex]
[tex]\implies x=\dfrac{4\pm2 }{2}[/tex]
[tex]\implies x=2\pm1[/tex]
[tex]\implies x=3, x=1[/tex]
Therefore, the points at which the curve crosses the x-axis are (3, 0) and (1, 0)
[tex]\\ \tt\hookrightarrow x^2-4x+3=0[/tex]
[tex]\\ \tt\hookrightarrow x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\\ \tt\hookrightarrow x=\dfrac{4\pm \sqrt{16-12}}{2}[/tex]
[tex]\\ \tt\hookrightarrow x=\dfrac{4\pm 2}{2}[/tex]
