mathmath333 one year ago Solve

1. mathmath333

\large \color{black}{\begin{align} &x^2+5|x|+6=0\\~\\ &x\in \mathbb{R}\hspace{.33em}\\~\\ \end{align}}

2. tkhunny

Eyeball problem. No Solution. $$x^{2}$$ is at least zero (0). $$5|x|$$ is at least zero (0). The entire expression CANNOT be less than 6. Done! Sometimes, they just jump out at you. No need to fret over them.

3. mathmath333

is there any other way to do this

4. TheSmartOne

If you graphed it, you would get: https://www.desmos.com/calculator/3bps8xaezl and you can tell that there will never be an x value that will make y=0 because the smallest value of y is 6.

5. TheSmartOne

And to explain what tkhunny said for others who don't understand what he said right away like myself. We have + 6 in the equation. So that means x^2 + x|5| has to equal -6 in order for the whole equation to be negative However, there will never be any x value that will make it -6. And since we have x^2, any value of x that goes into that will be positive And then there is 5|x| any x value plugged in will also come out as positive. So thus x^2+5|x| will never be negative. So it can not have any solutions.

6. ybarrap

Here's another way. $$x^2+5|x|+6=0$$ means for $$x\ge0$$ $$x^2+5|x|+6=x^2+5x+6=0$$ Which has solutions $$x=-3,x=-2$$. But $$x\ge0$$ so there is no solution. for $$x\le0$$ $$x^2+5|x|+6=x^2-5x+6=0$$ Which has solutions $$x=3,x=2$$. But $$x\le0$$ so there is no solution.

7. anonymous

Hi Use following tool to solve this problem http://www.acalculator.com/log.html

8. tkhunny

Another way? Why?! Shall we use the brute force of 7th grade algebra or whatever app someone wrote or shall we think and use good judgment and just be done? Note: On a GRE, LSAT, MCAT, or other significant examination, you WILL want the fast way.

9. mathmath333

teacher wont give me marks

10. tkhunny

Shame on that teacher. If you were my child, or a student under my tutelage, I would have words with that teacher. Logic is as valid as any other construct. Shameful. Simply shameful.