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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 Tags equation, properties, quadratic Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post bgh Linear Algebra 6 October 16th, 2017 12:11 PM shaharhada Algebra 2 August 30th, 2016 12:09 PM mich89 Algebra 3 January 9th, 2013 02:22 PM Ndjs Elementary Math 6 April 3rd, 2011 10:20 AM 123Peter Calculus 0 February 5th, 2011 05:09 AM

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