Question

Determine which polynomial can be rewritten to include the factor below.

(x -7 + 11i)
A. x2 - 14x + 170
B. x2 - 7x + 170
C. x2 - 7x + 121
D. x2 - 14x + 121

Answer 1

Answer:

Option A - $x^2-14x+170=0$    

Step-by-step explanation:

Given : The factor $(x-7+11i)$

To find : Determine which polynomial can be rewritten to include the factor below?

Solution :

A quadratic equation $ax^2+bx-c=0$ in which $b^2-4ac<0$ has two complex roots $x=\frac{-b+i\sqrt{b^2-4ac}}{2a},\frac{-b-i\sqrt{b^2-4ac}}{2a}$

So, There always exist a root with positive i and negative i.

So, one root of the polynomial is $(x-7+11i)$ then the other root must be $(x-7-11i)$          

Now, We have two roots so multiply them to find the polynomial.

$(x-7+11i)(x-7-11i)=0$      

$x^2-7x-11ix-7x+49+77i+11ix-77i-(11i)^2=0$          

$x^2-14x+49-121i^2=0$                      

$x^2-14x+49+121=0$          

$x^2-14x+170=0$          

Therefore, Option A is correct.