Find the value of $a^{2}+b^{2}+c^{2}-2ab+2ac-2bc$,if $a=x+y$,$b=x-y$,and $c=2x-1$.

The range of $a$ for which the roots of $x^2 - 2x - a^2 + 1 = 0$ lie between the roots (exclusive) of the equation $x^2 - 2(a + 1)x + a(a - 1) = 0$ is:

If $\alpha, \beta$ are the roots of $x^2 - 3x + a = 0, a \in R$ and $\alpha < 1 < \beta$,then:

If $ax^2 + bx + c = 0$ has real and distinct roots,$\alpha$ and $\beta$ $(\beta > \alpha)$. Further $a > 0, b < 0$ and $c < 0$ then :-

If the roots of the equation $({p^2} + {q^2}){x^2} - 2q(p + r)x + ({q^2} + {r^2}) = 0$ are real and equal,then $p, q, r$ will be in

If $a(p + q)^2 + 2bpq + c = 0$ and $a(p + r)^2 + 2bpr + c = 0$,then $qr$ =