Question

find the discriminant.
\\(8q^2 - 2q + 5 = 0\\)
what type of solutions does the equation have?
one real solution
two real solutions
two complex (non - real) solutions

Explanation:

Step1: Recall discriminant formula

For a quadratic equation \(ax^2 + bx + c = 0\), the discriminant \(D\) is \(D = b^2 - 4ac\).
Here, \(a = 8\), \(b = -2\), \(c = 5\).

Step2: Calculate discriminant

Substitute values into the formula:
\(D = (-2)^2 - 4\times8\times5\)
\(= 4 - 160\)
\(= -156\)

Step3: Determine solution type

If \(D > 0\), two real solutions; \(D = 0\), one real solution; \(D < 0\), two complex (non - real) solutions.
Since \(D=-156 < 0\), the equation has two complex (non - real) solutions.

Answer:

The discriminant is \(-156\). The equation has two complex (non - real) solutions.