Question

find the discriminant.
3p² + 5p + 9 = 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, \(a = 3\), \(b = 5\), \(c = 9\).

Step2: Calculate discriminant

Substitute values: \(D = 5^2 - 4\times3\times9\)
\(= 25 - 108\)
\(= -83\)

Step3: Determine solution type

If \(D > 0\): two real solutions.
If \(D = 0\): one real solution.
If \(D < 0\): two complex (non - real) solutions.
Since \(D=-83 < 0\), equation has two complex (non - real) solutions.

Answer:

Discriminant: \(-83\)
Type of solutions: two complex (non - real) solutions