If the sum of the roots of a quadratic equation is $-1$ and the sum of their reciprocals is $\frac{1}{6}$,then the equation is:

If for the function $f(x) = \frac{1}{4}x^2 + bx + 10$; $f(12 - x) = f(x)$ for all $x \in R$,then the value of $b$ is:

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3+p x^2+q x+r=0$,then the coefficient of $x$ in the cubic equation whose roots are $\alpha(\beta+\gamma), \beta(\gamma+\alpha)$ and $\gamma(\alpha+\beta)$ is

If the sum of the roots of the equation $ax^2 + bx + c = 0$ is equal to the sum of the reciprocals of their squares,then $bc^2, ca^2, ab^2$ will be in

If $\alpha$ and $\beta$ are the roots of the equation $a x^2+b x+c=0$ and if $p x^2+q x+r=0$ has roots $\frac{1-\alpha}{\alpha}$ and $\frac{1-\beta}{\beta}$,then $r$ is equal to

If the sum of the roots of the quadratic equation $ax^2 + bx + c = 0$ is equal to the sum of the squares of their reciprocals,then $a/c, b/a, c/b$ are in