Question

if the equation x^2-kx-36=0 has x=12 as one root what is the value of k?

Answer 1

That would mean f(12) = 0.

(12)² - 12k - 36 = 0

144 - 12k - 36 = 0

-12k = -108

k = 9

Answer 2

Another way of solving this problem is:

If x = 12 is a root, then x^2 - kx - 36 has to factor into (x - 12)(x + 3) since you need the 3 to multiply the -12 to give you -36.

(x - 12)(x + 3) = x^2 + 3x - 12x - 36 = x^2 - 9x - 36

When you compare x^2 - 9x - 36 with x^2 - kx - 36, you get k = 9.