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Prove that the equation Z^3+i Z-1=0 has ...

Prove that the equation `Z^3+i Z-1=0` has no real roots.

A

three real roots

B

one real roots

C

no real roots

D

no real or complex roots

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` Suppose `x` is real root.
Then `x^(3)+ix-1=0`
`impliesx^(3)-1=0` and `x=0`
`implies ` There is no real number satisfying these two equations.
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