Determine which polynomial can be rewritten to include the factor below.(x -7 + 11i) A. x2 - 14x + 170B. x2 - 7x + 170C. x2 - 7x + 121D. x2 - 14x + 121

Answer:Option A - [tex]x^2-14x+170=0[/tex]     Step-by-step explanation:Given : The factor [tex](x-7+11i)[/tex]To find : Determine which polynomial can be rewritten to include the factor below?Solution : A quadratic equation [tex]ax^2+bx-c=0[/tex] in which [tex]b^2-4ac<0[/tex] has two complex roots [tex]x=\frac{-b+i\sqrt{b^2-4ac}}{2a},\frac{-b-i\sqrt{b^2-4ac}}{2a}[/tex]So, There always exist a root with positive i and negative i.So, one root of the polynomial is [tex](x-7+11i)[/tex] then the other root must be [tex](x-7-11i)[/tex]           Now, We have two roots so multiply them to find the polynomial.[tex](x-7+11i)(x-7-11i)=0[/tex]       [tex]x^2-7x-11ix-7x+49+77i+11ix-77i-(11i)^2=0[/tex]           [tex]x^2-14x+49-121i^2=0[/tex]                      [tex]x^2-14x+49+121=0[/tex]          [tex]x^2-14x+170=0[/tex]          Therefore, Option A is correct.