Question

Write a polynomial equation of degree 4 in standard form that has the solutions i, −i, 1, −1.

Answer 1

Answer:

x⁴ + 2 x² + 1

Step-by-step explanation:

given solution of the polynomial

i, −i, 1, −1.                        

equation of the polynomial will be equal to

 =(x - i)(x + i)(x - 1)(x + 1)                      

 = (x² + i x - i x - i²)(x² + x - x + 1)            

 =(x² - (-1))(x² + 1 )                        

 = (x² + 1)(x² + 1)                        

= x⁴ + x² + x² + 1                          

= x⁴ + 2 x² + 1                                    

hence, the required polynomial equation is x⁴ + 2 x² + 1