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If ''$P$ implies $Q$"is false, how is $P$? How is $Q$? Use it to prove that

If $x$ is a real number satisfying $-3x^{2} + 2x + 8 = 0$, then $x> 0$ ''

it's false.

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    What do you know about [implications](https://en.wikipedia.org/wiki/Material_conditional)? Have you ever studied truth tables? See the column numbered "11" in this [truth table](https://en.wikipedia.org/wiki/Truth_table#Truth_table_for_all_binary_logical_operators) for a good idea of how P --> Q could be false. – 2017-01-28

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Step 1: find the solutions to $$-3x^2 + 2x + 8 = 0$$

There are two solutions. Are both of them $>0$?

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    No. One solution is positive (2) and another is negative! For this reason x>0 is false and "P implies Q" is false because P (the equation) are true and x>0 is false!! Is my answer correct? @TheChaz2.0 – 2017-01-28
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    You are correct. But are you the Original Poster? – 2017-01-28
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    No, I am not the poster. – 2017-01-28