Question

Solve.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

If $x=4$ is a root, then it should satisy the equation,

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

$4^2-9\left(4\right)+k=0$

$\therefore k=20$

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

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

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

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

$\therefore x=4,5$