The product of real roots of the equation $|x|^{6/5} - 26|x|^{3/5} - 27 = 0$ is:

The smallest positive integral value of $a$, for which all the roots of $x^4 - ax^2 + 9 = 0$ are real and distinct, is equal to

If each root of the equation $2x^3 + ax^2 - 8x + b = 0$ is reduced by $1$,then in the transformed equation thus formed,the term containing $x^2$ and the constant term vanish. The roots of the original equation are

In a triangle $ABC$,the value of $\angle A$ is given by $5\cos A + 3 = 0$. Find the quadratic equation whose roots are $\sin A$ and $\tan A$.

If a root of the equation $x^2 + px + 12 = 0$ is $4$,while the roots of the equation $x^2 + px + q = 0$ are equal,then the value of $q$ will be:

If $\alpha$ and $\beta$ are roots of the equation $x^2 - x + 1 = 0$,then $\alpha^{2009} + \beta^{2009} = \dots$