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Use the discriminant to determine the number of real-number solutions for the equation:

8x2 + 8x + 2 = 0

Aone solution
Btwo solutions
Cno solutions
Dinfinitely many solutions

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Answer:

A. One solution

Step-by-step explanation:

Given quadratic equation is,

\(8x^2+8x+2=0\)

Since, if for a quadratic equation \(ax^2+bx+c\),

The discriminant,

\(D=b^2-4ac > 0\)

The equation has two real different solutions,

If D = 0,

The equation has one real solution with multiplicity two,

While, if D < 0,

The equation has two imaginary solutions,

Here, the discriminant,

\(D=(8)^2-4\times 8\times 2=64-64 = 0\)

Thus, by the above explanation,

It is clear that the given equation has one real solution,

Option A is correct.

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