Answer:
Option B
[tex]x=4+9i[/tex] and [tex]x=4-9i[/tex]
Step-by-step explanation:
we have
[tex]x^{2} -8x+97=0[/tex]
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^{2} -8x+97=0[/tex]
so
[tex]a=1\\b=-8\\c=97[/tex]
substitute in the formula
[tex]x=\frac{-(-8)(+/-)\sqrt{-8^{2}-4(1)(97)}} {2(1)}[/tex]
[tex]x=\frac{8(+/-)\sqrt{-324}} {2}[/tex]
Remember that
[tex]i^{2} =-1[/tex]
[tex]i=\sqrt{-1}[/tex]
[tex]x=\frac{8(+/-)18i} {2}[/tex]
[tex]x=\frac{8(+)18i} {2}=4+9i[/tex]
[tex]x=\frac{8(-)18i} {2}=4-9i[/tex]
