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For what values of a does the equation (a^2 + 2a)x^2 + (3a)x+2 = 0 yield no real solutions x? Express your answer in interval notation.

 Oct 23, 2020
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no real solutions

For what values of a does the equation (a^2 + 2a)x^2 + (3a)x+2 = 0 yield no real solutions x? Express your answer in interval notation.

 

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\((a^2 + 2a)x^2 + (3a)x+2 = 0\\ \)

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

\(x = {-3a \pm \sqrt{\color{blue}9a^2-4\cdot (a^2+2a)\cdot 2} \over 2\cdot (a^2+2a)}\)    \(\color{blue}(9a^2-4\cdot (a^2+2a)\cdot 2)\ <\ 0\)   

 

The equation has no real solutions when \(a\in \mathbb{R}\ |0\ <\ a\ <\ 16 \)

laugh  !

 Oct 24, 2020

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