Answer:
[tex] \purple{ \boxed{ \bold{\therefore \: f(x) = {x}^{2} - 12x + 20 }}}[/tex]
Step-by-step explanation:
[tex]x = 10 \: \: and \: \: x = 2 \\ \therefore \: x - 10 = 0 \: \: and \: \: x - 2 = 0 \\let \: f(x) \: be \: the \: required \: function. \\\therefore \: f(x) = (x - 10)(x - 2) \\ \therefore \: f(x) = {x}^{2} + ( - 10 - 2)x + ( - 10)( - 2) \\ \red { \boxed{ \bold{\therefore \: f(x) = {x}^{2} - 12x + 20 }}}[/tex]
Hence, the function [tex] \orange { { \bold{\therefore \: f(x) = {x}^{2} - 12x + 20 }}}[/tex] has roots x = 10 and x = 2.
