Question

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))

Answer 1

`(x-(4+√(3)i))(x-(4-√(3)i)).`

Explanation:

First, find the roots of the polynomial
`x^2-8x+19:`

`D=(-8)^2-4\cdot 19=64-76=-12.`

Since
`i^2=-1,` then
`D=-12=12i^2.`

So,

`x_(1,2)=(-(-8)\pm √(12i^2))/(2)=(8\pm 2√(3)i)/(2)=4\pm √(3)i.`

Now the polynomial
`x^2-8x+19` is equivelent to

`(x-(4+√(3)i))(x-(4-√(3)i)).`