If $\left|\frac{x^2+kx+1}{x^2+x+1}\right| < 3$ for all real $x$,then $k$ is in the interval

If the expression $7+6x-3x^2$ attains its extreme value $\beta$ at $x=\alpha$,then the sum of the squares of the roots of the equation $x^2+\alpha x-\beta=0$ is

The number of real solution$(s)$ of the equation $x^2+3x+2=\min \{|x-3|, |x+2|\}$ is:

Let $\alpha, \beta$ be the roots of the equation $x^2 - 3x + r = 0$, and $\frac{\alpha}{2}, 2\beta$ be the roots of the equation $x^2 + 3x + r = 0$. If the roots of the equation $x^2 + 6x = m$ are $2\alpha + \beta + 2r$ and $\alpha - 2\beta - \frac{r}{2}$, then $m$ is equal to:

If the lengths of two sides of a triangle are the roots of the equation $x^2-2 \sqrt{3} x+2=0$ and the angle between these sides is $\frac{\pi}{3}$,then the perimeter of the triangle is

If $ax + by = 1$,where $a, b, x$ and $y$ are integers,then which one of the following is not true?