A graph of a cubic polynomial is plotted on a graph paper.

What is the sum of the roots of the polynomial?

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.

$6x^2-3-7x$

Verify that the numbers given alongside of the cubic polynomial below are their zeroes. Also, verify the relationship between the zeroes and coefficients.

$g\left(x\right)=x^3-4x^2+5x-2; 2, 1, 1$

$\alpha$ and $\beta$ are the zeros of the quadratic polynomial $f\left(x\right)=x^2-x-4$. If the value of $\frac{1}{\alpha }+\frac{1}{\beta }-\alpha \beta =k$, then find the value of $4k$.

Ankita got an electric wire and she wanted to bend the wire in a mathematical shape. She bent the wire in a shape of a parabola. A parabola has one of the two shapes either open upwards like $\cup$or open downwards like $\cap$. The shape made by Ankita is shown in the below figure:

Sabita got another electric wire whose shape is also a parabola. If the zeroes of Sabita's parabola are reciprocal to each other and the polynomial of it is $5x^2+26x+k$, then the value of $k$ is

Find the sum of the roots of the equation

$\frac{1}{x-3}-\frac{1}{x+5}=\frac{1}{6}$

Ajay, Ankit and Vijay respectively calculated the following polynomials with sum of the zeroes as $18$ and product of the zeroes as $81$.

$x^2-18x+81, x^2+18x-81, 2x^2-9x-81$

They discussed their solutions among themselves and pointed out mistakes in the calculations. Name the person whose calculation is correct.