Question

For the quadratic equation x2 + 2x + 8 = 0, find the value of the discriminant. Then, describe the number and type of roots for the equation. Finally, find the exact solution of the equation by using the Quadratic Formula.

Answer 1

ax^2 +bx+c=0
X^2 + 2x+8=0 so a=1, b=2, c=8

Discriminat= b^2 -4ac=2^2 -4•1•8=4-32=-28

So there are no real number solutions, yet there are complex numbers solutions.

Solutions=(-b+- sqrt (discriminant))/2•a
=(-2+-i sqrt ( 2•2•7))/2
Solutia 1= -1 + i sqrt7
Solutia 2= -1 - i sqrt 7