If $2 + i$ is a root of the equation ${x^3} - 5{x^2} + 9x - 5 = 0$, then the other roots are
$1$ and $2 - i$
$-1$ and $3 + i$
$0$ and $1$
$-1$ and $i - 2$
The number of ordered pairs $(x, y)$ of real numbers that satisfy the simultaneous equations $x+y^2=x^2+y=12$ is
The roots of the equation ${x^4} - 4{x^3} + 6{x^2} - 4x + 1 = 0$ are
Let $\alpha$ and $\beta$ be the roots of $x^2-6 x-2=0$, with $\alpha>\beta$. If $a_n=\alpha^n-\beta^n$ for $n \geq 1$, then the value of $\frac{a_{10}-2 a_8}{2 a_9}$ is
The number of real values of $x$ for which the equality $\left| {\,3{x^2} + 12x + 6\,} \right| = 5x + 16$ holds good is
The number of solutions for the equation ${x^2} - 5|x| + \,6 = 0$ is