Question 1: Solve for x: 2x² + 3x - 2 = 0.

Answer: x = 0.5 or x = -2

Question 2: Solve for x: -x² + 4x - 3 = 0.

Answer: x = 1 or x = 3

Question 3: Solve for x: 3x² = 12.

Answer: x = 2 or x = -2√3

Question 1: A student attempts to solve x² - 5x + 6 = 0 using the quadratic formula and writes x = [ -(-5) ± √( (-5)² - 4×1×6 ) ] / 2×1. Identify and correct any mistake in the calculation.

Answer: The student forgot to simplify the discriminant √(25 - 24) = √1 correctly; solution is x = (5 ± 1)/2 → x=3 or x=2

Question 2: Explain why a negative discriminant (e.g., from 2x² + 4x + 5 = 0) leads to complex solutions and why students should check the discriminant before solving.

Answer: A negative discriminant indicates no real solutions; students should recognize this early to avoid incorrect calculations.

Question 1: A ball is thrown upward so that its height (in meters) after t seconds is given by h(t) = -5t² + 20t + 2. When does the ball hit the ground? Use the quadratic formula to find the time.

Answer: t = 0.2 seconds and t = 2 seconds

Question 1: Solve the quadratic equation: 4x² + 4x + 1 = 0. Explain if the solutions are real or complex.

Answer: x = -0.5 (double root); solutions are real and equal

Question 2: Given the quadratic x² - kx + 16 = 0, find the value of k if the solutions are imaginary.

Answer: k² < 64

Question 1: A student solves 3x² + 6x + 2 = 0 and writes the solutions as x = (-6 ± √(36 - 24)) / 3. Is this correct? If not, fix the error.

Answer: The discriminant is √(36 - 24) = √12, which is correct; solutions are x = (-6 ± √12)/6.

Question 2: A student forgets to consider the discriminant when solving 2x² + 4x + 5 = 0. Why is this mistake significant?

Answer: Without checking the discriminant, the student might attempt to find real solutions when none exist, leading to errors.