Consider the following statement in respect of the polynomial $a(b-c)(x-b)(x-c)+b(c-a)(x-c)(x-a)+c(a-b)(x-a)(x-b):$

1. The coefficient of $x^2$ is $0.$

2. The coefficient of $x$ is $(a-b)(b-c)(c-a).$

Which of the statements given above is/are correct?

Consider the following two statements
$\mathrm{I}$. Any pair of consistent liner equations in two variables must have a unique solution.
$\mathrm{II}$. There do not exist two consecutive integers, the sum of whose squares is $365$ .

Then

If one of the zeroes of the quadratic polynomial $x^2+3x+k$ is $2$, then find the value of $k$ is

If $\alpha , \beta$ and $\gamma$ are the zeros of a cubic polynomial $p\left(x\right)=a{x}^3+b{x}^2+cx+d, a\ne 0$ then $\frac{1}{\alpha }+\frac{1}{\beta }+\frac{1}{\gamma }=$ _____.

The sum of the zeroes of the polynomial $p\left(x\right)=5x^2+2x-3$ is