Question

If function ghas the factors (x-7) and (x + 6), what are the zeros of function ?

Answer 1

The zeros of function g are 7 and -6

Solution:

Given that function g has factors (x - 7) and (x + 6)

To find: zeros of function

The factor theorem is a theorem linking factors and zeros of a polynomial

The Factor Theorem states that  (x – a) is a factor of the polynomial f(x) if and only if f(a) = 0

That is, g(c) = 0 if and only if x - c is a factor

Since g(x) = (x - 7)(x + 6) then g(7) = 0 and g( -6 ) = 0

Since those two x values output 0, then those x values are called the zeros

[ g(7) = (7 - 7)(7 + 6) = 0 and g(-6) = (-6 - 7)(-6 + 6) = 0]

Thus the zeros of function g are 7 and -6