A circle has a centre $\mathrm{O}$ and radii $\mathrm{OQ}$ and $\mathrm{OR}$. Two tangents, $\mathrm{PQ}$ and $\mathrm{PR}$, are drawn from an external point $\mathrm{P}$.

In addition to the above information, which of these must also be known to conclude that the quadrilateral $\mathrm{PQOR}$ is a square?

i) $\mathrm{OQ}$ and $\mathrm{OR}$ are at an angle of $90°$.

ii) The tangents meet at an angle of $90°$.

Write a quadratic polynomial whose sum of zeroes is less than that of polynomial 

Shown below is a part of the graph of a polynomial $h\left(x\right)$

On dividing $h\left(x\right)$ by which of the following, the remainder will be zero?

$\left(\mathrm{i}\right) \left(x-2\right)$

$\left(\mathrm{ii}\right) \left(x+2\right)$

$\left(\mathrm{iii}\right) \left(x-4\right)$

$\left(\mathrm{iv}\right) \left(x+4\right)$

Shown below are the parts of graphs of two polynomials, $g\left(x\right)$ and $h\left(x\right)$. When $h\left(x\right)$ is divided by $\left(x-3\right)$, the remainder is $k$

Which of these is true for the remainder when $g\left(x\right)$ is divided by $\left(x-3\right)$?

If $\alpha$ and $\beta$ are the zeroes of polynomial $x^2+8x+6$. Form a polynomial whose zeroes are $\alpha -\beta \text{and} \alpha +\beta$.