Question

Find a polynomial function​ f(x) of least degree having only real coefficients with zeros of​ 0, i and 1+i

Answer 1

The polynomial function with zeroes of 0, i and (1+i) is;. = x³ -(1 + 2√-1) + (√1 -1)x

The zeros of the polynomial are; 0, i and 1+i.

In essence, the factors of the polynomial are;

• (x -0), (x-i) and (x -1 -i)

The polynomial to be determined is therefore obtained by finding the product of the factors as follows;

• (x -0) (x-i) (x -1 -i)

• = x (x² -x -ix -ix +i +i²)

• = x (x² -x -2ix +i + i²)

• = x³ -x² -2ix² + ix + -x

• = x³ - (1+2i)x² + (i -1)x

Recall, i = √-1

= x³ -(1 + 2√-1) + (√1 -1)x

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