# Thread: completeness axiom

1. ## completeness axiom

if $a\neq 0$ and $b^2-4ac>0$ then prove that the equation :

$ax^2 +bx +c =0$ has a root,by using the completeness axiom in real Nos

2. The solution of any of this kind of equations is:

$x_{1,2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

so if u have

$a\neq 0$

and

$b^2-4ac>0$

then x1 and x2 will be real numbers.

Have a nice day,

Hush_Hush

3. 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 $a\neq 0$

and $b^2-4ac>0$ :

$\frac{- b\pm\sqrt{b^2-4ac}}{2a}$ exists??