Answer :
Answer:
[tex]x^2-6x+10[/tex]
Step-by-step explanation:
We know that the imaginary number i = [tex]\sqrt{-1}[/tex] and thus [tex]i^2=\sqrt{-1} \sqrt{-1} =-1[/tex]
If roots are given in the form (a+bi) and (a-bi), to find the quadratic, we can write it in the form:
(x - (a+bi) ) * (x - (a-bi))
and then multiply to figure out the answer. Shown below:
[tex](x-(3+i))(x-(3-i))\\=(x-3-i)(x-3+i)\\=x^2-3x+ix-3x+9-3i-ix+3i-i^2\\=x^2-6x+9-i^2\\=x^2-6x+9-(-1)\\=x^2-6x+9+1\\=x^2-6x+10[/tex]
Thus, the BLANK is -6x