Complex Solutions of Quadratics Test – Algebra 2 Math (Printable PDF)

Question 1 Discriminants (2 points)

For each equation, find the discriminant and state whether the solutions are two real, one real, or non-real.

1. x² − 10x + 25 = 0
2. 2x² + x − 15 = 0
3. x² − 2x + 8 = 0
4. 4x² + 4x + 5 = 0

(2 points)

Question 2 Squared binomial equation (2 points)

Solve (x − 5)² = −36.

Question 3 Quadratic formula (3 points)

Solve 3x² + 2x + 7 = 0. Write each solution in the form p ± qi with exact values.

Question 4 Completing the square (3 points)

Solve x² + 8x + 41 = 0 by completing the square.

Question 5 Range of a constant (2 points)

Find all values of k for which x² + 6x + k = 0 has non-real solutions.

Question 6 A graph and its equation (2 points)

The graph of y = x² + 2x + 5 is shown.

1. How many real solutions does x² + 2x + 5 = 0 have? Explain using the graph. (1 point)
2. Solve the equation. (1 point)

Question 7 Writing an equation (3 points)

One solution of a quadratic equation with real coefficients is 2 + 7i.

1. State the other solution. (1 point)
2. Find the sum and the product of the two solutions. (1 point)
3. Write the equation in the form x² + bx + c = 0. (1 point)

Question 8 Will the drone reach the height? (3 points)

A drone released from a 6-foot platform has height h(t) = −16t² + 20t + 6 feet after t seconds. A sensor sits 15 feet above the ground.

1. Write the equation that gives the times when the height is 15 feet in the form at² + bt + c = 0. (1 point)
2. Use the discriminant to decide whether the drone reaches the sensor. (1 point)
3. Solve the equation. (1 point)