Answer:
C. [tex]f(x)=(x-(7-i))(x-(5+i))(x-(7+i))(x-(5-i))[/tex]
Step-by-step explanation:
We want to find the equation of a polynomial the following properties;
i. Leading coefficient is 1
ii. roots (7 + i) and (5 – i) with multiplicity 1
Recall the complex conjugate properties of the roots of a polynomial.
According to this property, if
[tex]a+bi[/tex] is a root of a polynomial, then the complex conjugate, [tex]a-bi[/tex] is also a root.
This means that:
(7 - i) and (5 + i) with multiplicity 1 are also roots of this polynomial.
The complete set of roots are:
[tex]x=(7+i),x=(7-i),x=(5-i),x=(5+i)[/tex]
Therefore the polynomial is:
[tex]f(x)=(x-(7-i))(x-(5+i))(x-(7+i))(x-(5-i))[/tex]
The correct choice is C.
Answer:
C. f(x)= (x-(7-i)) (x-(5+i))(x-(7+i))(x-(5-i)
Step-by-step explanation:
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