The product of all real roots of the equation ${x^2} - |x| - \,6 = 0$ is
$-9$
$6$
$9$
$36$
Let $x, y, z$ be positive reals. Which of the following implies $x=y=z$ ?
$I.$ $x^3+y^3+z^3=3 x y z$
$II.$ $x^3+y^2 z+y z^2=3 x y z$
$III.$ $x^3+y^2 z+z^2 x=3 x y z$
$IV.$ $(x+y+z)^3=27 x y z$
The number of solutions for the equation ${x^2} - 5|x| + \,6 = 0$ is
Let $\alpha, \beta, \gamma$ be the three roots of the equation $x ^3+ bx + c =0$. If $\beta \gamma=1=-\alpha$, then $b^3+2 c^3-3 \alpha^3-6 \beta^3-8 \gamma^3$ is equal to $......$.
If $x$ is real , the maximum value of $\frac{{3{x^2} + 9x + 17}}{{3{x^2} + 9x + 7}}$ is
The number of distinct real roots of the equation $x^{5}\left(x^{3}-x^{2}-x+1\right)+x\left(3 x^{3}-4 x^{2}-2 x+4\right)-1=0$ is