Question

find the discriminant.
$8w^2 - 7 = 0$
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 \(D = b^2 - 4ac\).
In the equation \(8w^2 - 7 = 0\), we have \(a = 8\), \(b = 0\) (since there is no \(w\) term), and \(c = -7\).

Step2: Calculate the discriminant

Substitute \(a = 8\), \(b = 0\), and \(c = -7\) into the discriminant formula:
\(D = 0^2 - 4\times8\times(-7)\)
\(D = 0 + 224\)
\(D = 224\)

Step3: Determine the type of solutions

Since the discriminant \(D = 224>0\), a quadratic equation with a positive discriminant has two distinct real solutions.

Answer:

The discriminant is \(224\), and the equation has two real solutions.