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# Algebra

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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.

!

Apr 10, 2022
edited by asinus  Apr 10, 2022