Question 180002
Let's see if your answer checks:
{{{x = (1 +-sqrt(15)i)/8}}}
I'll plug 1 of these 2 answers back into the equation
{{{4x^2 - x + 1 = 0}}}
{{{4*((1 + sqrt(15)i)/8)^2 - (1 + sqrt(15)i)/8 + 1 = 0}}}
{{{4*(1 + 2*sqrt(15)i + 15*i^2)/64 - 1/8 - sqrt(15)i/8 + 1 = 0}}}
{{{1/16 + (sqrt(15)i)/8 - 15/16 - 1/8 - sqrt(15)i/8 + 1 = 0}}}
multiply both sides by {{{16}}}
{{{1 + 2*(sqrt(15)i) - 15 - 2 - 2*(sqrt(15)i) + 16 = 0}}}
{{{1 - 15 - 2 + 16 = 0}}}
{{{17 - 17 = 0}}}
The other root should check out, too. I'll let you do it.