find the discriminant of the following equation to determine the number and type of solutions it will have 3f-9f^2=6

Answer 1

discriminant = b^2 - 4ac

rewrite the equation in ax^2+bx+ c = 0 form

-9f^2 +3f - 6 =0

then the discriminant

= 3^2 -4(-9)(-6)= 9-216 = -207<0

if the discriminant < 0, then there are 2 imaginary solutions. Zero real solutions

use the quadratic formula

f=1/6 + or - (i/6)(sqr23)

f= (1+sqr23)/6