If $x$ is real, then the value of $\frac{{{x^2} + 34x - 71}}{{{x^2} + 2x - 7}}$ does not lie between
$-9$ and $-5$
$-5$ and $9$
$0$ and $9$
$5$ and $9$
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
If $\alpha, \beta$ are roots of the equation $x^{2}+5 \sqrt{2} x+10=0, \alpha\,>\,\beta$ and $P_{n}=\alpha^{n}-\beta^{n}$ for each positive integer $\mathrm{n}$, then the value of $\left(\frac{P_{17} P_{20}+5 \sqrt{2} P_{11} P_{19}}{P_{18} P_{19}+5 \sqrt{2} P_{18}^{2}}\right)$ is equal to $....$
The roots of the equation ${x^4} - 4{x^3} + 6{x^2} - 4x + 1 = 0$ are
The equation $x^2-4 x+[x]+3=x[x]$, where $[x]$ denotes the greatest integer function, has:
The condition that ${x^3} - 3px + 2q$ may be divisible by a factor of the form ${x^2} + 2ax + {a^2}$ is