If the ratio of the roots of the equations $x^2 + bx + c = 0$ and $x^2 + qx + r = 0$ are equal,then:

If the sum of two roots of $x^3+p x^2+q x-5=0$ is equal to its third root,then $p(p^2-4q)=$

Let $a$ and $b$ be two non-zero real numbers. If $p$ and $r$ are the roots of the equation $x^{2}-8ax+2a=0$ and $q$ and $s$ are the roots of the equation $x^{2}+12bx+6b=0$,such that $\frac{1}{p}, \frac{1}{q}, \frac{1}{r}, \frac{1}{s}$ are in $A$.$P$.,then $a^{-1}-b^{-1}$ is equal to $......$

If $f(x) = 2x^3 + mx^2 - 13x + n$ and $2, 3$ are roots of the equation $f(x) = 0$,then the values of $m$ and $n$ are $-$

If $\alpha, \beta$ are the roots of $a x^2+b x+c=0$,then the quadratic equation whose roots are $\sqrt{5} \alpha, \sqrt{5} \beta$ is

If the ratio of the roots of $ax^2 + 2bx + c = 0$ is the same as the ratio of the roots of $px^2 + 2qx + r = 0$,then