Question

find the discriminant.
3x² + 6x + 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 a quadratic equation \(ax^2 + bx + c = 0\), the discriminant \(D = b^2 - 4ac\). Here, \(a = 3\), \(b = 6\), \(c = 3\).

Step2: Calculate discriminant

Substitute values: \(D = 6^2 - 4\times3\times3 = 36 - 36 = 0\).

Step3: Determine solution type

If \(D = 0\), the quadratic has one real solution (a repeated root).

Answer:

Discriminant is \(0\), and the equation has one real solution.