Question

若α、β为实系数二次方程ax^2+bx+c=0的两虚根,且α^2/b属于R,则α/β为

选项A.-1+-2分之根号3i B.+-1/2-2分之根号3i C.-2分之根号3+-1/2i D.+-2分之根号-1/2i

Answer 1

α=C+mi
β=C-mi
α+β=2C=-b/a
C=-b/2a
αβ=C^2+m^2=c/a
m^2=c/a-b^2/4a^2
=(4ac-b^2)/4a^2

α/β=(C+mi)^2/(C^2+m^2)
=(C^2+2Cmi-m^2)/(c/a)
=(-c/a+2Cmi)/(c/a)
=-1+2b根号(4ac-b^2)i/4a*a/c
=-1+bc根号(4ac-b^2)i/2

or =-1-bc根号(4ac-b^2)i/2

so,选A
写得有点乱，不懂可以再问的

Answer 2

有可能是α/β=b(1-√b^2-4ac)/2ac-1