What is the value of k for which the sum of the squares of the roots of $$2{x^2} - 2(k - 2)x - (k + 1) = 0$$ is minimum?

If the roots of the equation $$a(b - c){x^2} + b(c - a)x + c(a - b) = 0$$ are equal, then which one of the following is correct?

If $$\left| {{x^2} - 3x + 2} \right| > {x^2} - 3x + 2$$, then which one of the following is correct?

What re the roots of the equation $$\left| {{x^2} - x - 6} \right| = x + 2$$?