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Find all possible values of a, if the equations ax^2+5x+1=4x^2+7x-4 has two different real roots

 Apr 10, 2022
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Find all possible values of a, if the equations ax^2+5x+1=4x^2+7x-4 has two different real roots

 

Hello Guest!

 

\(ax^2+5x+1=4x^2+7x-4\\ ax^2-4x^2+5x-7x+1+4=0\\ (a-4)x^2-2x+5=0\)

\(a\in\mathbb R\ |\)  \(-\infty\)  \(<\)  \(a\)  \(<\ 4.2\)  \(and\) \(\ a\neq 4\)

With \(a\in\{4,4.2\}\), the equations have only one real root.

laugh  !

 Apr 10, 2022
edited by asinus  Apr 10, 2022

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