1
Question
z1,z2 are the roots of the equation z2+az+b=0. Let z1, z2 and the origin be the vertices of an equilateral triangle. Then a2−3b=
Open in App
Solution
The correct option is B 0
For equilateral Δ, z21+z22+z23−z1z2−z2z3−z3z1=0
We have z3=0,
∴z21+z22−z1z2=0--------------------------(1)
z1 & z2 are roots of z2+az+b
∴z1+z2=−a
z1z2=b
∴z21+z22=a2−2b
putting the values in equation 1
a2−2b−b=0
∴a2−3b=0
For equilateral Δ,
z21+z22+z23−z1z2−z2z3−z3z1=0
We have z3=0,
∴z21+z22−z1z2=0--------------------------(1)
z1 & z2 are roots of z2+az+b
∴z1+z2=−a
z1z2=b
∴z21+z22=a2−2b
putting the values in equation 1
a2−2b−b=0
∴a2−3b=0
We have z3=0,
∴z21+z22−z1z2=0--------------------------(1)
z1 & z2 are roots of z2+az+b
∴z1+z2=−a
z1z2=b
∴z21+z22=a2−2b
putting the values in equation 1
a2−2b−b=0
∴a2−3b=0
Suggest Corrections
0
Similar questions
View More
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
