Question

2. How many real number solutions are there to the equation 0 = –3x² + x – 4? (1 point)

Answer 1

given

`- 3 {x}^(2) + x - 4`
finding the determinant will tell us how many solutions
the determinant is

`{b}^(2) - 4ac`
so we have
a=-3
b=1
c=-4

so the determinant is

`{1}^(2) - 4( - 3)( - 4) = 1 - 48 = - 47`
now we know if d=0 there is 1 real solution if d<0 there are complex solutions and if d>0 there are 2 real solutions.
since d=-47<0 there are no real solutions only complex ones