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Q.

Assertion (A) : The origin and the roots of
the equation x2+ax+b=0 form an equilateral
triangle if a2=3b

Reason (R) : If z1,z2,z3 are vertices of an equilateral
triangle then z12+z22+z32=z1z2+z2z3+z3z1

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a

Both A and R are true R is correct
explanation to A

b

Both A and R are true but R is not correct
explanation to A

c

A is true R is false

d

A is false R is true

answer is A.

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Detailed Solution

Let z1, z2 be the roots of x2+ax+b=0

z1+z2=-a,       z1 z2=b,

0, z1, z2 forms equilateral triangle if

z12+z22=z1 z2 z12+z22+2z1 z2=3z1 z2 z1+z22=3z1 z2   a2=3b  

Both A, R are true and RA

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