Each of the roots of the equation $x^3-6x^2+6x-5=0$ are increased by $h$. If the new transformed equation does not contain the $x^2$ term,then $h$ is equal to:

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

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+3x^2-10x-24=0$,and $\alpha(\beta+\gamma), \beta(\gamma+\alpha), \gamma(\alpha+\beta)$ are the roots of the equation $x^3+px^2+qx+r=0$,then $q=$

If $2+\sqrt{3}$ is a root of the equation $f(x)=x^4+2x^3-16x^2-22x+7=0$,then which one of the following is not a root of $f(x)=0$?

The quadratic equation with real coefficients whose one root is $7 + 5i$ will be:

The value of $m$ for which the equation $\frac{a}{x + a + m} + \frac{b}{x + b + m} = 1$ has roots equal in magnitude but opposite in sign is