An algebra problem by vedit kumawat

$\Rightarrow x(x-k)=k+1$

$x^2-kx-k+1=0$

$x^2-k(x+1)+1=0$

Using Vieta's Formula.

Sum of roots = $\boxed{k}$

Any quadratic equations in x with two roots a and b can be expressed as, (x - a)(x - b) = 0. Which on expansion takes the form, x² - (a + b)x - ab = 0

Hence, the sum of the roots = -(coefficient of x in the expanded form)

Now, x(x - k) = k + 1 => x² - kx - (k + 1) = 0

Hence, sum of the roots = -(-k) = k