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

Solve the equation $x^{2}+3x+5=0$.

Let $\theta$,$0 < \theta < \pi / 2$,be an angle such that the equation $x^2 + 4x \cos \theta + \cot \theta = 0$ has equal roots for $x$. Then $\theta$ in radians is

Let $S$ be the set of all real roots of the equation $3^{x}(3^{x}-1)+2=|3^{x}-1|+|3^{x}-2|$. Then $S$

If for any real $x$,$y = \frac{11 x^2+12 x+6}{x^2+4 x+2}$ is such that $y < a$ or $y \geq b$,then $a, b$ are

If $\alpha, \beta$ are the roots of $ax^{2}+bx+c=0$ $(a \neq 0)$ and $\alpha+h, \beta+h$ are the roots of $px^{2}+qx+r=0$ $(p \neq 0),$ then the ratio of the squares of their discriminants is