Question

Determine which expression could represent a polynomial with a factor of (x - √3i)

Answer 1

Option (3)

Explanation:

`(x-i√(3))` is a factor of a polynomial given in the options, that means a polynomial having factor as
`(x-i√(3))` will be 0 for the value of x =
`i√(3)`.

Option (1),

3x⁴ + 26x² - 9

=
`3(i√(3))^(4)+26(i√(3))^2-9` [For x =
`i√(3)`]

= 3(9i⁴) + 26(3i²) - 9

= 27 - 78 - 9 [Since i² = -1]

= -60

Option (2),

4x⁴- 11x² + 3

=
`4(i√(3))^4-11(i√(3))^2+3`

= 4(9i⁴) - 33i² + 3

= 36 + 33 + 3

= 72

Option (3),

4x⁴ + 11x² - 3

=
`4(i√(3))^4+11(i√(3))^2-3`

= 4(9i⁴) + 33i² - 3

= 36 - 33 - 3

= 0

Option (4),

`3x^(4)-26x^(2)-9`

=
`3(i√(3))^4-26(i√(3))^(2)-9`

= 3(9i⁴) - 26(3i²) - 9

= 27 + 78 - 9

= 96

Therefore,
`(x-i√(3))` is a factor of option (3).