Question

If $x=4$ is a root of $x^2-9x+k=0$, find the value of $k$ and hence find the other root.

Answer 1

$f\left(x\right)=x^2-9x+k=0$

$\Rightarrow f\left(4\right)=4^2-9\times 4+k=0$ since $x=4$ is a root.

$\Rightarrow 16-36+k=0$

$\Rightarrow k-20=0$

$\therefore k=20$

To find the other root:

$x^2-9x+k=0$ becomes $x^2-9x+20=0$ since $k=20$

$x^2-9x+20=0$

$\Rightarrow x^2-5x-4x+20=0$

$\Rightarrow x(x-5)-4(x-5)=0$

$\Rightarrow (x-5)(x-4)=0$

$\therefore x=5,4$

Hence the other root is $5$