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# no real solutions

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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

#1
+11086
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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.

Hello Guest!

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

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

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

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

!

Oct 24, 2020