If the roots of the equation $8{x^3} - 14{x^2} + 7x - 1 = 0$ are in $G.P.$, then the roots are
$1,\frac{1}{2},\frac{1}{4}$
$2, 4, 8$
$3, 6, 12$
None of these
Let $f(x)=a x^2+b x+c$, where $a, b, c$ are integers, Suppose $f(1)=0,40 < f(6) < 50,60 < f(7) < 70$ and $1000 t < f(50) < 1000(t+1)$ for some integer $t$. Then, the value of $t$ is
If $\alpha $ and $\beta $ are the roots of the quadratic equation, $x^2 + x\, sin\,\theta -2sin\,\theta = 0$, $\theta \in \left( {0,\frac{\pi }{2}} \right)$ then $\frac{{{\alpha ^{12}} + {\beta ^{12}}}}{{\left( {{\alpha ^{ - 12}} + {\beta ^{ - 12}}} \right){{\left( {\alpha - \beta } \right)}^{24}}}}$ is equal to
The roots of the equation ${x^4} - 2{x^3} + x = 380$ are
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
The number of real solutions of the equation $3\left(x^2+\frac{1}{x^2}\right)-2\left(x+\frac{1}{x}\right)+5=0$, is