Question

How to write a polynomial function with the roots 1-2i and 1+2i

Answer 1

f(x) = x²- 2x +5

Explanation:

- The difference of squares identity can be written:

a² - b² = ( a - b ) ( a + b )

Use this with a = ( x − 1 ) and b = 2 i as follows:

f(x) = ( x − 1 − 2i ) ( x − 1 + 2i )

= ( ( x − 1 ) − 2i ) ( ( x − 1 ) + 2i )

= ( x − 1 )² − ( 2i )²

= x² − 2x + 1 + 4

f(x) = x²- 2x +5

Any polynomial in x with these zeros will be a multiple (scalar or polynomial) of this f ( x )