Question

determine the discriminant of the quadratic equation. use the value of the discriminant to determine whether the equation has two real solutions, one repeated real solution, or two complex solutions that are not real.

\\4z^2 + 11z + 11 = 0\\

discriminant =

Explanation:

⚡ Using what you learned: quadratic formula and its applications

Step 1: Identify Coefficients

For the quadratic equation \( 4z^2 + 11z + 11 = 0 \):

$$ a = 4, \quad b = 11, \quad c = 11 $$

Step 2: Calculate the Discriminant

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

$$ D = 11^2 - 4(4)(11) $$

$$ D = 121 - 176 $$

$$ D = -55 $$

Step 3: Determine the Number and Type of Solutions

Since the discriminant is negative (\( D < 0 \)), the equation has two complex solutions that are not real.

Answer:

discriminant = -55; two complex solutions that are not real