If 5 is a zero of the polynomial f(x) = ax² − (2a + 1)x − 5, then the value of a is

Explanation

Since 5 is a zero of f(x) = ax² − (2a + 1)x − 5, we have f(5) = 0. Thus 25a − 5(2a + 1) − 5 = 0, so 25a − 10a − 5 − 5 = 0. Hence 15a = 10 and a = 2/3.