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

Option (3)

Step-by-step explanation:

is a factor of a polynomial given in the options, that means a polynomial having factor as will be 0 for the value of x = .

Option (1),

3x⁴ + 26x² - 9

= [For x = ]

= 3(9i⁴) + 26(3i²) - 9

= 27 - 78 - 9 [Since i² = -1]

= -60

Option (2),

4x⁴- 11x² + 3

=

= 4(9i⁴) - 33i² + 3

= 36 + 33 + 3

= 72

Option (3),

4x⁴ + 11x² - 3

=

=  4(9i⁴) + 33i² - 3

= 36 - 33 - 3

= 0

Option (4),

=

= 3(9i⁴) - 26(3i²) - 9

= 27 + 78 - 9

= 96

Therefore, is a factor of option (3).

x² + 11x + 18 < 0  

[-11 ± sqrt(121 - 72)]/2 = (-11 ± 7)/2  

solution: (-9, -2)

step-by-step explanation: