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

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