If the roots of $4x^2 + px + 9 = 0$ are equal,then the absolute value of $p$ is:

Let $\alpha, \beta, \gamma, \delta$ be the roots of the equation $x^4 + x^2 + 1 = 0$. Then the equation whose roots are $\alpha^2, \beta^2, \gamma^2, \delta^2$ is:

The number of real roots of the equation $\frac{(x^2+1)^3}{x^3} + \frac{x^2+1}{3x} = 0, (x \neq 0)$ is

If $2 \sin^3 x + \sin 2x \cos x + 4 \sin x - 4 = 0$ has exactly $3$ solutions in the interval $[0, \frac{n \pi}{2}]$,$n \in N$,then the roots of the equation $x^2 + nx + (n-3) = 0$ belong to :

The number of real roots of the equation $x |x| - 5|x + 2| + 6 = 0$ is:

If the roots of $x^2 - bx + c = 0$ are two consecutive integers,then $b^2 - 4c$ is