Find a third-degree polynomial f(x) with integer coefficients and with

Margie Marx

Margie Marx

Answered question

2021-12-09

Find a third-degree polynomial f(x) with integer coefficients and with zeros of 2 + i and .

Answer & Explanation

SlabydouluS62

SlabydouluS62

Skilled2021-12-10Added 52 answers

Step 1 
Given data is : 
Zeroes are (2+i) and 0 
Find the polynomial of third degree f(x)
Step 2 
One of the provided roots is intricate. There are complex roots in conjugate pairs
If one roots is 2+i then other roots is (2-i) 
Therefore zeroes are (2+i), (2-i) and 0 
Polynomial f(x) is given as 
f(x)=(x-0)(x-(2+i))(x-(2-i)) 
=x[(x-2)-i][(x-2)+i] 
=x[(x2)2i2] 
=x(x24x+4+1)   (i2=1) 
=x(x24x+5) 
Therefore , the polynomial f(x) is x(x24x+5)

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