"find all real solutions" 5x^4+29x^3-x^2+29x-6 = 0

HELP PLEASE PRECAL IS SO HARD!

Question

"find all real solutions" 5x^4+29x^3-x^2+29x-6 = 0


HELP PLEASE PRECAL IS SO HARD!

solomonzelman · Answer

$\large\color{black}{ \displaystyle 5x^4+29x^3-x^2+29x-6=\left(5x-1\right)\left(x+6\right)\left(x^2+1\right)}$

solomonzelman · Answer

After factoring, you can solve for x by solving three separate cases.

*{1}*         $\large\color{black}{ \displaystyle \left(5x-1\right)=0\[0.5em] }$
*{2}*         $\large\color{black}{ \displaystyle \left(x+6\right)=0\[0.5em]}$
*{3}*         $\large\color{black}{ \displaystyle \left(x^2+1\right)=0\[0.5em]}$

solomonzelman · Answer

If you are *not* considering any *imaginary* solutions,
then case *{3}* will not have any solutions.