Question

determine the discriminant of the quadratic equation. use the value
\\3z^2 + 3z + 4 = 0\\

discriminant = \\(-39\\)

determine the number of solution(s) the quadratic equation has.

a. two rational solutions
b. two complex solutions that are not real
c. two irrational solutions
d. one repeated real solution

Explanation:

⚡ Using what you learned: quadratic formula and its applications

Step 1: Identify Coefficients

For the quadratic equation \(3z^2 + 3z + 4 = 0\):

$$a = 3, \quad b = 3, \quad c = 4$$

Step 2: Calculate the Discriminant

The discriminant formula is \(D = b^2 - 4ac\):

$$D = 3^2 - 4(3)(4)$$

$$D = 9 - 48$$

$$D = -39$$

Step 3: Determine the Number and Type of Solutions

Since the discriminant is negative (\(D < 0\)), the square root in the quadratic formula yields an imaginary number. This means the equation has two complex solutions that are not real.

Answer:

discriminant = \(-39\)

Number of solution(s): B. two complex solutions that are not real