Question

find the discriminant.
3w² - 5w + 3 = 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, \(a = 3\), \(b = -5\), \(c = 3\).

Step2: Calculate discriminant

Substitute values: \(D = (-5)^2 - 4\times3\times3 = 25 - 36 = -11\).

Step3: Determine solution type

If \(D < 0\), two complex (non - real) solutions; \(D = 0\), one real solution; \(D>0\), two real solutions.
Since \(D=-11 < 0\), equation has two complex solutions.

Answer:

Discriminant: \(-11\); Type of solutions: two complex (non - real) solutions