If $\operatorname{cosec} \theta$ and $\cot \theta$ are the roots of $cx^2+bx+a=0$ $(bc \neq 0)$,then $b^2(b^2-4ac)=$

Two real numbers $\alpha$ and $\beta$ are such that $\alpha + \beta = 3$ and $|\alpha - \beta| = 4$. Then $\alpha$ and $\beta$ are the roots of the quadratic equation:

If $p$ and $q$ are the roots of the equation $x^{2}+px+q=0$,then:

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 + 2x - 5 = 0$ and the equation $x^3 + bx^2 + cx + d = 0$ has roots $2\alpha + 1, 2\beta + 1, 2\gamma + 1$,then the value of $|b + c + d|$ is (where $b, c, d$ are constants):

Let $\alpha$ and $\beta$ be two distinct roots of the equation $x^3 + 3x^2 - 1 = 0$. The equation which has $(\alpha \beta)$ as its root is equal to

If $\alpha, \beta, \gamma$ are the roots of the equation $3x^3 - 9x^2 + 5x - 7 = 0$,then what is the value of $\alpha + \beta + \gamma$?