Which of the following representations of a quadratic has complex roots?

The quadratic equation that has complex roots is the equation;

B, 9·x² + 33 = 0

Step-by-step explanation:

The given quadratic equation are;

A. 2·(x + 3)² = 64

B. 9·x² + 33 = 0

C. (x, y)

(-2.5, 2), (-2, 0), (-1.5, -1), (-1, -1), (-0.5, 0), (0, 2)

D. A graph with x-intercept at (2, 0)

Analyzing each of the quadratic equations, we have;

For A

2·(x + 3)² = 64 gives;

(x + 3)² = 64/2 = 32

(x + 3)² = 32 = (4·√2)²

∴ (x + 3)² = (4·√2)²

(x + 3) = ±4·√2

x = 4·√2 - 3 or x = -4·√2 - 3 which are real numbered roots

For option B we have;

9·x² + 33 = 0

9·x²  = -33

9·x² = (3·x)² = -33

(3·x)² = -33

3·x = ±√(-33)

x = ±√(-33)/3 = ± √(-1)×(√33)/3 which has complex root √(-1)

For option C we have;

The roots of the equation occurs at y = 0 which corresponds with the points (-2, 0) and (-0.5, 0), therefore, the equation has real roots

For option C we have;

The roots of the equation occurs at y = 0 which is found as the point (2, 0) therefore, the equation has real roots

36 is the final answer! : )

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)