For what value of $\mathrm{k}$, is $3$ a zero of the polynomial $2{\mathrm{x}}^2+\mathrm{x}+\mathrm{k}$ ?

For what value of $\mathrm{k}$, is $-3$ a zero of the polynomial ${\mathrm{x}}^2+11\mathrm{x}+\mathrm{k}$?

If a quadratic polynomial $f\left(x\right)$ is factorisable into linear distinct factors, then what is the total number of real and distinct zeroes of $f\left(x\right)$?

If $f\left(x\right)$ is a polynomial such that $f\left(a\right)f\left(b\right)<0$, then what is the number of zeros lying between $a$ and $b$?

If the graph of quadratic polynomial $a{x}^2+bx+c$ cuts the positive direction of $y\mathit{-}axis$, then what is the sign of $c$?