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

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- Apr 18th 2009, 10:27 AMxalkcompleteness axiom
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 - Apr 18th 2009, 10:55 AMHush_Hush
The solution of any of this kind of equations is:

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

so if u have

$\displaystyle a\neq 0$

and

$\displaystyle b^2-4ac>0$

then x1 and x2 will be real numbers.

Have a nice day,

Hush_Hush - Apr 18th 2009, 02:30 PMxalk
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??