![\begin{gathered} x-\text{intercepts: } \\ x=\text{ 1+ }\frac{2}{\sqrt[]{5}}\text{ or x = 1- }\frac{2}{\sqrt[]{5}} \\ x\text{ = 1.894 or x = 0.106} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/2rdqi9j77mo8m1dff1m17j37al0xgk8a14.png)
Step-by-step explanation:
quadratic function: y = 5(x-1)² - 4
x intercept is gotten when y = 0
representing y with 0 in the quadratic function , we solve for x
0 = 5(x-1)² - 4
collect like terms by adding 4 to both sides:
0+ 4 = 5(x-1)² - 4 + 4
4 = 5(x-1)²
divide both sides by 5:

4/5 = (x-1)²
square root both sides:
![\begin{gathered} \sqrt[]{(4)/(5)}=\sqrt[]{(x-1)^2} \\ \pm\sqrt[]{(4)/(5)}=\text{ x-1} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/hp7lgq3xdaz2v36mqunbycpr6a24ksxko8.png)
simplify:
![\begin{gathered} x\text{ - 1 = }\pm\sqrt[]{(4)/(5)} \\ x\text{ =1}\pm\text{ }\sqrt[]{(4)/(5)}\text{ = 1}\pm\text{ }\frac{\sqrt[]{4}}{\sqrt[]{5}} \\ x\text{ = 1}\pm\text{ }\frac{2}{\sqrt[]{5}} \\ x\text{ = 1+ }\frac{2}{\sqrt[]{5}}\text{ or x = 1- }\frac{2}{\sqrt[]{5}} \\ x\text{ = 1+ 0}.894\text{ or x = 1-0.894} \\ x\text{in tercept: } \\ x\text{ = 1.894 or x = 0.106} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/sp7xp14ax41hnxmi6kl409ro4wmdr3kpbc.png)