Question

Find `K`, if `x^2-2x+k` has `x-1` as a factor?

Answer 1

`k=1`

Explanation:

If `(x-1)` is a factor of `x^2-2x+k` then `x=1` is a zero, so:

`0 = (color(blue)(1))^2-2(color(blue)(1))+k`

`color(white)(0) = 1-2+k = k - 1`

So `k=1`

Another way to see this is:

`x^2-2x+k = x^2-2x+1+k-1 = (x-1)^2+(k-1)`

This is divisible by `(x-1)` if and only if the remainder `(k-1) = 0`