If the four roots of the equation z4+z3+2z2+z+1=0 form a quadrilateral on the Argand plane, then the area of the quadrilateral is
A
√3+28
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B
√3+24
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C
√3+22
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D
√3+23
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Solution
The correct option is B√3+24 z4+z3+2z2+z+1=0 On dividing the equation by z2, z2+1z2+z+1z+2=0 ⇒(z+1z)2+(z+1z)=0 ⇒z+1z=0 or z+1z+1=0 ⇒z=±i or z=ω,ω2 where ω is cube root of unity.
Now, plotting solution on Argand plane,
The quadrilateral is a trapezium. Thus, required area =12×(2+√3)×12=√3+24