Question

if x-3 is a factorof x^2+kx+9 then find the valueofk

Answer 1

$f(x) = {x}^{2} + kx + 9 \\ g(x) = x - 3 \\ x - 3 = 0 \\ x = 3 \\(3) {}^{2} + k(3) + 9 = 0 \\ 9 + k3 + 9 = 0 \\ k3 + 18 =0 \\ k3 = - 18 \\ k = \frac { - 18}{3} \\ k = - 6 \\ answer$

Answer 2

$x - 3 \: is \: factor \: of \: {x}^{2} + kx + 9 \\ we \: know \: that \\ x - 3 = 0 \\ x = 3 \\ put \: the \: value \: of \: x \\ (3) {}^{2} + k3 + 9 = 0 \\ 9 + 3k + 9 = 0 \\ 18 + 3k = 0 \\ 18 = - 3k \\ k = - 6$