Question

Which polynomial function has a leading coefficient of 1 and roots (7 + i) and (5 – i) with multiplicity 1?

Answer 1

Answer:

C. $f(x)=(x-(7-i))(x-(5+i))(x-(7+i))(x-(5-i))$

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

$a+bi$ is a root of a polynomial, then the complex conjugate, $a-bi$  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:

$x=(7+i),x=(7-i),x=(5-i),x=(5+i)$

Therefore the polynomial is:

$f(x)=(x-(7-i))(x-(5+i))(x-(7+i))(x-(5-i))$

The correct choice is C.

Answer 2

Answer:

C. f(x)= (x-(7-i)) (x-(5+i))(x-(7+i))(x-(5-i)

Step-by-step explanation:

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