If the roots of the quadratic equation $x^2-35x+c=0$ are in the ratio $2:3$ and $c=6K$,then $K=$

If the harmonic mean between the roots of $(5+\sqrt{2}) x^2-b x+(8+2 \sqrt{5})=0$ is $4$,then the value of $b$ is

If the roots of the equation $x^2 + bx + c = 0$ are reciprocals of each other,then...

Let $f(n)=A(-2)^n+B(-3)^n$ for all $A, B \in \mathbb{R}$ and $n \in \mathbb{N}-\{1, 2\}$. If $f(n)+a f(n-1)+b f(n-2)=0$,then $(a+b)(b-a)=$

If $\alpha, \beta, \gamma$ and $\delta$ are the roots of the equation $x^4+3x^3-6x^2+2x-4=0$,then find the equation having roots $\frac{1}{\alpha}, \frac{1}{\beta}, \frac{1}{\gamma}$ and $\frac{1}{\delta}$.

If the roots of the equation $x^2 + px + q = 0$ differ by $1$,then: