if $\displaystyle a\neq 0$ and $\displaystyle b^2-4ac>0$ then prove that the equation :
$\displaystyle ax^2 +bx +c =0$ has a root,by using the completeness axiom in real Nos
I am sorry, you have misread my post, i said prove the existence by using the completeness axiom.
To use the square root you must prove 1st that it exists.
How do you know that for all a, b, c and such that $\displaystyle a\neq 0$
and $\displaystyle b^2-4ac>0$ :
$\displaystyle \frac{- b\pm\sqrt{b^2-4ac}}{2a}$ exists??