Practice problem
Let ω\omegaω be a non-real number such that ω3=1\omega^3 = 1ω3=1. Mark all true statements below.
If a,b,ca,b,ca,b,c are real numbers such that aω2+bω+c=0a\omega^2+b\omega+c = 0aω2+bω+c=0, then a=b=ca=b=ca=b=c.
If a,b,ca,b,ca,b,c are real numbers such that a=b=ca=b=ca=b=c, then aω2+bω+c=0a\omega^2+b\omega+c = 0aω2+bω+c=0.
There exist real numbers a,b,ca,b,ca,b,c, not all equal, such that aω2+bω+c=0a\omega^2+b\omega+c = 0aω2+bω+c=0.
There exist real numbers a,b,ca,b,ca,b,c such that a=b=ca=b=ca=b=c, yet aω2+bω+c≠0a\omega^2+b\omega+c \neq 0aω2+bω+c=0.
Type a concept, like “slope” or “photosynthesis”.