contestada

Which of the following is equivalent to the polynomial below?
x^2-8x+19

A.) (x+(4-3i)) (x+(4-3i))
B.) (x+(4+3i)) (x+(4-3i))
C.) (x-(4+3i)) (x-(4-3i))
D.) (x+(4+3i)) (x-(4-3i))

Respuesta :

frika

Answer:

[tex](x-(4+\sqrt{3}i))(x-(4-\sqrt{3}i)).[/tex]

Step-by-step explanation:

First, find the roots of the polynomial [tex]x^2-8x+19:[/tex]

[tex]D=(-8)^2-4\cdot 19=64-76=-12.[/tex]

Since [tex]i^2=-1,[/tex] then [tex]D=-12=12i^2.[/tex]

So,

[tex]x_{1,2}=\dfrac{-(-8)\pm \sqrt{12i^2}}{2}=\dfrac{8\pm 2\sqrt{3}i}{2}=4\pm \sqrt{3}i.[/tex]

Now the polynomial [tex]x^2-8x+19[/tex] is equivelent to

[tex](x-(4+\sqrt{3}i))(x-(4-\sqrt{3}i)).[/tex]