Question

What are the zeros of f(x) = x - 10x+ 25?

O A. x= -5 only
O B. x = 5 only
O c. x= -5 and x = 5
D. x= -5 and x = 10

Answer 1

Given Expression,

`\sf \: f(x) = {x}^(2) - 10x + 25`

The above expression is of the form (a - b)² = a² - 2ab + b²

Thus,

`\implies \: \sf \: f(x) = (x) {}^(2) - 2(5)x + {5}^(2) \\ \\ \implies \: \sf \: f(x) = (x - 5) {}^(2)`

Equating f(x) = 0,

`\implies \: \sf \: (x - 5) {}^(2) = 0 \\ \\ \implies \: \sf \: x - 5 = 0 \\ \\ \implies \: \boxed{ \boxed{ \sf x = 5}}`

Option (B) is correct