If the equation having the roots as the values obtained by diminishing each root of the equation $x^3-3x^2+2x-1=0$ by $K$ is $x^3-x-1=0$,then $K=$

Let $\alpha, \beta$ be the roots of the equation $ax^2 + 2bx + c = 0$ and $\gamma, \delta$ be the roots of the equation $px^2 + 2qx + r = 0$. If $\alpha, \beta, \gamma, \delta$ are in $G.P.$,then:

If $3p^2 = 5p + 2$ and $3q^2 = 5q + 2$,where $p \ne q$,then $pq$ is equal to

The two roots of the equation $x^3 - 9x^2 + 14x + 24 = 0$ are in the ratio $3 : 2$. Find the roots.

The condition that one root of the equation $ax^2 + bx + c = 0$ is three times the other is:

Two candidates attempt to solve the equation $x^2 + px + q = 0$. One starts with a wrong value of $p$ and finds the roots to be $2$ and $6$,and the other starts with a wrong value of $q$ and finds the roots to be $2$ and $-9$. The roots of the original equation are