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May 1st, 2019, 12:02 PM   #1
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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 12:18 PM.
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May 1st, 2019, 01:43 PM   #2
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$D\gt 0$ means two real solutions. The question is a little ambiguous.
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May 1st, 2019, 08:06 PM   #3
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$(b^2 - 4ac)/a^2 > 0$
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