The roots of the function [tex]f(x)=x^2-2x-35[/tex] are x = -5 and x = 7
The given function is:
[tex]f(x)=x^2-2x-35[/tex]
This can be further simplified as:
[tex]f(x)=x^2-7x+5x-35[/tex]
Factoring the common terms in the expression above:
[tex]f(x) = x(x-7)+5(x-7)[/tex]
Grouping common terms together
[tex]f(x)=(x-7)(x+5)[/tex]
Let f(x) be zero in order to find the roots of the function
[tex](x-7)(x+5)=0[/tex]
Equate each of the factors to zero
x - 7 = 0
x = 7
x + 5 = 0
x = -5
The roots of the function [tex]f(x)=x^2-2x-35[/tex] are x = -5 and x = 7
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