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 $(b - c)x^2 + (c - a)x + (a - b) = 0$ are equal,then $a, b, c$ are in which progression?

The number of positive real roots of the equation $3^{x+1}+3^{-x+1}=10$ is

If a polynomial $f(x)$ is divided by $(x + 1)$,$(x - 2)$,and $(x + 2)$,the remainders are $6$,$3$,and $15$ respectively. Find the remainder when $f(x)$ is divided by $(x + 1)(x - 2)(x + 2)$.

The midpoint of the diagonal of a rectangle formed by $x^2+5x-6=0$ and $y^2-8y-20=0$ is

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