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If $a, b, c$ are three real numbers such that $a + b + c = 0$ (at least one $a, b, c$ is not equal to zero) and $a z_{1} + b z_{2} + c z_{3} = 0,$ then $z_{1}, z_{2}, z_{3}$ :

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Correct option is A

az1+bz2+cz3=0, a+b+c=0. at least one of a, b, c≠0 and a, b,c∈R . Let a≠0 Then z1=bz2+cz3b+c [∵ −a=b+c] Thus, z1 divides the line segment joining z2 and z3 in the ratioc : b and therefore z1,z2,z3 are collinear

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If a, b, c are three real numbers such that a+b+c=0 (at least one a, b, c is not equal to zero) and az1+bz2+cz3=0, then z1,z2,z3 :

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Ready to Test Your Skills?

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If $a, b, c$ are three real numbers such that $a + b + c = 0$ (at least one $a, b, c$ is not equal to zero) and $a z_{1} + b z_{2} + c z_{3} = 0,$ then $z_{1}, z_{2}, z_{3}$ :