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May 1st, 2019, 01:02 PM  #1 
Senior Member Joined: Dec 2015 From: Earth Posts: 833 Thanks: 113 Math Focus: Elementary Math  Quadratic Equation Properties
Given equation $\displaystyle ax^2 +bx +c =0\; $ ; $\displaystyle a,b,c \in \mathbb{R}$ . Find the relation of coefficients a,b,c in a single relation such that the equation has two real solutions . Or find the function $\displaystyle F(a,b,c)=0$ such that the condition holds true (two real solutions ). What I think is $\displaystyle F(a,b,c)=a+b+c=0$ . The most used and known relation is $\displaystyle D=b^2  4ac >0$ , but how to find the relation above ? Last edited by idontknow; May 1st, 2019 at 01:18 PM. 
May 1st, 2019, 02:43 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,855 Thanks: 744 
$D\gt 0$ means two real solutions. The question is a little ambiguous.

May 1st, 2019, 09:06 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 21,124 Thanks: 2332 
$(b^2  4ac)/a^2 > 0$


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equation, properties, quadratic 
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