Question

find the zero of the polynomial f(x)=(x-5)2-(x+5)2​

Answer 1

Answer:

$f(x) = {(x - 5)}^{2} - {(x + 5)}^{2} \\ using \: identity \\ {a}^{2} - {b}^{2} = (a + b)(a - b) \\ where \\ a = x - 5 \: \: and \: \: \: b = x + 5 \\ then \\ f(x) = (x - 5 + x + 5)(x - 5 - x - 5) \\ = 2x( - 10) = - 20x$

$if \: \: f(x) = - 20x = 0 \\ then \\ x = 0$