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for the equation |{:(1,,x,,x^(2)),(x^(2...

for the equation `|{:(1,,x,,x^(2)),(x^(2),,1,,x),(x,,x^(2),,6):}|=0`

A

There are exactly two distinct roots

B

there is one pair of equation real roots

C

There are three pairs of equal roots

D

Modulus of each root is 2

Text Solution

Verified by Experts

The correct Answer is:
C
`Delta = (1+ x+x^(2)) |{:(1,,1,,1),(x^(2),,1,,x),(x,,x^(2),,1):}| =(1-x^(3))^(2)`
Therefore `Delta =0` has roots `1,1 ,omega, omega, omega^(2),omega^(2)`
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