ikavumacj
2021-12-03
Knes1997
Beginner2021-12-04Added 11 answers
To find the polynomial with real coefficients
Assume that f(x) is a polynomial with real coefficients, with I and (1+i) as its zeros.Since the zeroes i and (1+i) are complex number and so its conjugates are also the zeroes of the polynomial f(x) with the real coefficient.
So, the zeroes of the polynomial f(x) are -i,i, (1+i) and (1-i).
Then, the polynomial f(x) will be of degree 4.
If a is a zero of the polynomial f(x), then (x-a) is a factor of the polynomial f(x).
So,
f(x)=[x-(1+i)][x-(1-i)](x-i)(x+i)
(Since, )
Hence, the required polynomial with the real coefficient of the smallest possible degree is
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