Question

Use the discriminant to determine the number of real-number solutions for the equation:
8x2 + 8x + 2 = 0
A. one solution
B. two solutions
C. no solutions
D. infinitely many solutions

Answer 1

If the discriminant = 0 there is only 1 solution.
If the discriminant > 0 there are 2 solutions.
If the disciminant < 0 there are 0 solution.

Answer 2

We should also remember that the discriminant of a function Ax^2 + Bx + C = 0 is defined to be: B^2 - 4AC. :)

Answer 3

@hinarauf80
As @jtvatsim wrote:
If the discriminant = 0 there is only 1 solution.

So, for 8x2 + 8x + 2 = 0
A. one solution

Not two solutions
@Luis_Rivera

Answer 4

actually , its a double root. thats what i refered to

Answer 5

@Luis_Rivera
Thanks for the response. I apologize for my error.

The Fundamental Theorem of Algebra escaped my mind. Yes, there are two roots here. They are not distinct but there are two.

Fundamental Theorem of Algebra: A polynomial of degree n has exactly n roots when the domain is the set of complex numbers.