If the equation $2x^3 + 5x^2 - 4x - 12 = 0$ has a repeated root,then the constant term of the quadratic equation whose roots are the distinct roots of the given equation is

The quadratic equation whose roots are three times the roots of $3ax^2+3bx+c=0$ is

Let $f(x)=ax^{2}+bx+c$ and $g(x)=px^{2}+qx+r$ such that $f(1)=g(1)$,$f(2)=g(2)$ and $f(3)-g(3)=2$. Then,$f(4)-g(4)$ is:

If the set of all $a \in R - \{1\}$,for which the roots of the equation $(1-a)x^2 + 2(a-3)x + 9 = 0$ are positive,is $(-\infty, -\alpha] \cup [\beta, \gamma)$,then $2\alpha + \beta + \gamma$ is equal to . . . . . . .

Let $[x]$ be the greatest integer less than or equal to $x$ for a real number $x$. Then the equation $[x^2] = x + 1$ has:

If $AM$ and $GM$ of roots of a quadratic equation are $5$ and $4$,respectively,then the quadratic equation is