Shown below are the graphs of two cubic polynomials, $f\left(x\right)$ and $g\left(x\right)$. Both the polynomials have the zeroes $-1, 0$ and $1$

Anya said, " Both the graphs represent the same polynomial, $f\left(x\right)=g\left(x\right)=\left(x+1\right)\left(x-0\right)\left(x-1\right)$ as they have the same zeroes.

Pranit said," Both the graphs represent two different polynomial, $f\left(x\right)=\left(x+1\right)\left(x-0\right)\left(x-1\right)$ and $g\left(x\right)=-\left(x+1\right)\left(x-0\right)\left(x-1\right)$ and only two such polynomial exist that can have the zeroes $-1, 0$ and $1$

Aadar said, " Both the graphs represent two different polynomial and infintely many such polynomials exist that have zeroes $-1, 0$ and $1$.

Who is right and justify your answer?

$p\left(x\right)=2x^2-6x-3$. The two zeroes are of the form: $\frac{3\pm \sqrt{k}}{2}$; where $k$ is a real number.

Use the relationship between the zeroes and the coefficients of a polynomial to find the value of $k$. Show your steps.

Two polynomials are shown in the graph below. Find the number of zeroes that are common to both polynomials. Explain your answer.

$\frac{x^2-3\sqrt{2}x+4}{x-\sqrt{2}}$;  $x\ne \sqrt{2}$

At how many points does the graph of the above expression intersect the $x$ axis? Show your work.

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 $\left(x-3\right)$?