Question

determine the discriminant of the quadratic equation.

\\3z^2 + 3z + 4 = 0\\

discriminant =

Explanation:

⚡ Using what you learned: quadratic formula and its applications

Step 1: Identify coefficients

Identify the coefficients \(a\), \(b\), and \(c\) from the standard form quadratic equation \(az^2 + bz + c = 0\):

$$ 3z^2 + 3z + 4 = 0 $$

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

Step 2: Calculate the discriminant

The formula for the discriminant is:

$$ D = b^2 - 4ac $$

Substitute the values of \(a\), \(b\), and \(c\):

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

$$ D = 9 - 48 $$

$$ D = -39 $$

Answer:

-39