Question 719865
{{{sqrt(-9)+8}}}
{{{sqrt(9*(-1))+8}}}
{{{sqrt(9)*sqrt(-1)+8}}}
3*i+8
8 + 3i<br>
If the discriminant, {{{b^2-4ac}}}, is a perfect square then the quadratic will factor (i.e. it is not prime). If the discriminant is not a perfect square then the quadratic is prime.<br>
For {{{x^2-x-1}}} the discriminant is:
{{{(-1)^2-4(1)(-1) = 1-4(1)(-1) = 1+4 = 5}}}
5 is not a perfect square so {{{x^2-x-1}}} is prime.