OMG I BEG PLS SOMEONE HELP ME

Question

What is the discriminant and number of real solutions of -8x² + 9x - 4 = 0

Answer 1

-8x^2 + 9x - 4 = 0

the discriminant is b^2 -4ac = 9^2 -4(-8)(-4) = 81-128 =- 47 <0

if the discriminant is less than zero there are no real solutions

8x^2 -9x +4 = 0

x = 18/16 + or - (1/16)sqr(81-128)

x= 9/8 + or - (i/16)sqr47

there are two imaginary solutions

if you used descartes' rule of signs, that would show a potential maximum two positive real solutions, either 0,1, or 2, but that's consistent with zero real solutions. 0<2.

rule of signs shows zero possible negative real solutions

by deduction just on rule of signs there are either 2 real positive solutions or 2 imaginary solutions.

Answer turns out: 2 imaginary solutions, just by looking at the discriminant.

discriminant is b^2 -4ac where y=ax^2 +bx + c

a = -8, b=9, c= -4

b^2 -4ac = 9^2-4(-8)(-4) = 81-128 = -47<0