Let $x_1, x_2, \ldots, x_6$ be the roots of the polynomial equation $x^6+2 x^5+4 x^4+8 x^3+16 x^2+32 x+64=0$. Then,
$\left|x_i\right|=2$ for exactly one value of $i$
$\left|x_i\right|=2$ for exactly two values of $i$
$\left|x_i\right|=2$ for all values of $i$
$\left|x_i\right|=2$ for no value of $i$
The number of the real roots of the equation $(x+1)^{2}+|x-5|=\frac{27}{4}$ is ....... .
The smallest value of ${x^2} - 3x + 3$ in the interval $( - 3,\,3/2)$ is
The number of positive integers $x$ satisfying the equation $\frac{1}{x}+\frac{1}{x+1}+\frac{1}{x+2}=\frac{13}{2}$ is.
$\alpha$, $\beta$ ,$\gamma$ are roots of equatiuon $x^3 -x -1 = 0$ then equation whose roots are $\frac{1}{{\beta + \gamma }},\frac{1}{{\gamma + \alpha }},\frac{1}{{\alpha + \beta }}$ is
The sum of the cubes of all the roots of the equation $x^{4}-3 x^{3}-2 x^{2}+3 x+1=10$ is