Let $f(x)$ be a quadratic polynomial with $f(2)=10$ and $f(-2)=-2$. Then,the coefficient of $x$ in $f(x)$ is

If the roots of the equation $a(b - c)x^2 + b(c - a)x + c(a - b) = 0$ are equal,then $a, b, c$ are in

If $m, n$ are the roots of the equation ${x^2} - x - 1 = 0$,then the value of $\frac{{\left( {1 + m{{\log }_e}3 + \frac{{{{(m{{\log }_e}3)}^2}}}{{2!}} + ...\infty } \right)\left( {1 + n{{\log }_e}3 + \frac{{{{(n{{\log }_e}3)}^2}}}{{2!}} + ...\infty } \right)}}{{\left( {1 + mn{{\log }_e}3 + \frac{{{{(mn{{\log }_e}3)}^2}}}{{2!}} + ...\infty } \right)}}$ is:

The sum of all the real values of $x$ satisfying the equation $(x^2-7x+11)^{x^2-6x-7}=1$ is

The roots of the equation $|x - 2|^2 + |x - 2| - 6 = 0$ are:

The value of $k$ for which the equation $2x^2 - kx + x + 8 = 0$ has equal and real roots is: