a polynomial f(x) with real coefficients and leading

Answered question

2022-05-15

a polynomial f(x) with real coefficients and leading coefficients 1 has the given zero(s) and degree. Express f(x) as a product of linear and quadratic polynomials with real coefficients 0,-2i,1-i; degree 5

Answer & Explanation

user_27qwe

user_27qwe

Skilled2022-07-02Added 375 answers

Let f(x)  be the polynomial and containing the roots 0, -2i, 1-i
We know that if xi=a+ib is one root then other root must be a-ib.

+2i,1+i are also roots of f(x)

f(x)=(x-0)(x+2i)(x-2i)(x-1+i)(x-1-i)

         =x(x2+4)(x2-2x+2)

f(x)=x(x2+4)(x2-2x+2)

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