The number of real values of $x$ for which the equality $\left| {\,3{x^2} + 12x + 6\,} \right| = 5x + 16$ holds good is
$4$
$3$
$2$
$1$
Let $\alpha_1, \alpha_2, \ldots, \alpha_7$ be the roots of the equation $x^7+$ $3 x^5-13 x^3-15 x=0$ and $\left|\alpha_1\right| \geq\left|\alpha_2\right| \geq \ldots \geq\left|\alpha_7\right|$. Then $\alpha_1 \alpha_2-\alpha_3 \alpha_4+\alpha_5 \alpha_6$ is equal to $..................$.
If the roots of the equation $8{x^3} - 14{x^2} + 7x - 1 = 0$ are in $G.P.$, then the roots are
The number of distinct real roots of $x^4-4 x^3+12 x^2+x-1=0$ is
In the real number system, the equation $\sqrt{x+3-4 \sqrt{x-1}}+\sqrt{x+8-6 \sqrt{x-1}}=1$ has