If the sum of the two roots of the equation $4{x^3} + 16{x^2} - 9x - 36 = 0$ is zero, then the roots are
$1, 2 -2$
$ - 2,\frac{2}{3}, - \frac{2}{3}$
$ - 3,\frac{3}{2}, - \frac{3}{2}$
$ - 4,\frac{3}{2}, - \frac{3}{2}$
If $\alpha , \beta , \gamma $ are roots of equation ${x^3} + a{x^2} + bx + c = 0$, then ${\alpha ^{ - 1}} + {\beta ^{ - 1}} + {\gamma ^{ - 1}} = $
Consider the quadratic equation $n x^2+7 \sqrt{n x+n}=0$ where $n$ is a positive integer. Which of the following statements are necessarily correct?
$I$. For any $n$, the roots are distinct.
$II$. There are infinitely many values of $n$ for which both roots are real.
$III$. The product of the roots is necessarily an integer.
If $\alpha ,\beta ,\gamma $are the roots of the equation ${x^3} + x + 1 = 0$, then the value of ${\alpha ^3}{\beta ^3}{\gamma ^3}$
If the roots of ${x^2} + x + a = 0$exceed $a$, then
The polynomial equation $x^3-3 a x^2+\left(27 a^2+9\right) x+2016=0$ has