The number of real roots of the polynomial equation $x^4-x^2+2 x-1=0$ is
$0$
$2$
$3$
$4$
Let $\alpha$ and $\beta$ be the roots of the equation $5 x^{2}+6 x-2=0 .$ If $S_{n}=\alpha^{n}+\beta^{n}, n=1,2,3 \ldots$ then :
The value of $x$ in the given equation ${4^x} - {3^{x\,\; - \;\frac{1}{2}}} = {3^{x + \frac{1}{2}}} - {2^{2x - 1}}$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.
The complete solution of the inequation ${x^2} - 4x < 12\,{\rm{ is}}$
The solution set of the equation $pq{x^2} - {(p + q)^2}x + {(p + q)^2} = 0$ is