Question

find the discriminant.
6v² - 3v - 2 = 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 quadratic equation \(ax^2 + bx + c = 0\), discriminant \(D = b^2 - 4ac\).
Here, \(a = 6\), \(b = -3\), \(c = -2\).

Step2: Calculate discriminant

Substitute values: \(D = (-3)^2 - 4\times6\times(-2)\)
\(= 9 + 48\)
\(= 57\)

Step3: Determine solution type

Since \(D = 57>0\), quadratic has two real solutions.

Answer:

Discriminant: \(57\); Type of solutions: two real solutions