Question

$2x^5+x^4-2x-1=0$
solve

Answer 1

$\mathrm{Factor\:}2x^5+x^4-2x-1:\quad \left(2x+1\right)\left(x^2+1\right)\left(x+1\right)\left(x-1\right)$

$\mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)$

$\mathrm{Solve\:}\:2x+1=0:\quad x=-\frac{1}{2}$

$\mathrm{Solve\:}\:x^2+1=0:\quad x=i,\:x=-i$

$\mathrm{Solve\:}\:x+1=0:\quad x=-1$

$\mathrm{Solve\:}\:x-1=0:\quad x=1$

$x=-\frac{1}{2},\:x=i,\:x=-i,\:x=-1,\:x=1$