Question

find the discriminant.
\\(2x^2 - 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 \(D = b^2 - 4ac\).
In the equation \(2x^2 - 5 = 0\), \(a = 2\), \(b = 0\), \(c = -5\).

Step2: Calculate discriminant

Substitute \(a = 2\), \(b = 0\), \(c = -5\) into the discriminant formula:
\(D = 0^2 - 4\times2\times(-5)\)
\(= 0 + 40\)
\(= 40\)

Step3: Determine solution type

Since the discriminant \(D = 40>0\), a quadratic equation with a positive discriminant has two distinct real solutions.

Answer:

The discriminant is \(40\). The equation has two real solutions.