Both the roots of the given equation $(x - a)(x - b) + (x - b)(x - c) + (x - c)(x - a) = 0$ are always

If $A$ and $G$ represent the arithmetic mean and geometric mean respectively,and $x^2 - 2Ax + G^2 = 0$,then which of the following is true?

If the equation $2x^2 - kx + x + 8 = 0$ has equal and real roots,then the value of $k$ will be .....

If the roots of the given equation $(\cos p-1) x^2+(\cos p) x+\sin p=0$ are real,then

If $P(x) = ax^2 + bx + c$ and $Q(x) = -ax^2 + dx + c$ where $ac \neq 0$,then $P(x) \cdot Q(x) = 0$ has at least:

If roots of the equation $ax^2 + bx + c = 0$ are $(\alpha - \beta)$ and $(\gamma - \delta)$,and roots of the equation $Ax^2 + Bx + C = 0$ are $(\alpha + \delta)$ and $(\beta + \gamma)$,then $\left| \frac{a}{A} \right|$ is equal to (where $D_1$ and $D_2$ are discriminants of the given equations respectively).