If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f\left(x\right)=a{x}^2+bx+c$, then evaluate: $\alpha -\beta$.

If $\alpha -\beta =k$, then find $\frac{\sqrt{b^2-4ac}}{k}$ ?.

$\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f\left(x\right)=a{x}^2+bx+c$. If ${\alpha }^2\beta +\alpha {\beta }^2=\frac{k}{a^2}$, then, find the value of $k$.

If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f\left(x\right)=a{x}^2+bx+c$, if $\frac{{\left(b^2-2ac\right)}^2-a^4\left({\alpha }^4+{\beta }^4\right)}{a^2{c}^2}=k$, find the value of $k$.

If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f\left(x\right)=a{x}^2+bx+c$, then evaluate $\frac{1}{a\alpha +b}+\frac{1}{a\beta +b}$.

If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f\left(x\right)=a{x}^2+bx+c$, then evaluate: $\frac{\beta }{a\alpha +b}+\frac{\alpha }{a\beta +b}$

If $\frac{\beta }{a\alpha +b}+\frac{\alpha }{a\beta +b}=k$, then what is the value of $\left(\frac{-a}{2}\right)k$

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

$f\left(x\right)=2x^3+x^2-5x+2; \frac{1}{2}, 1, -2$