Question 1: Solve for x: 2x² + 5x - 3 = 0 using the quadratic formula.

Answer: x = 0.5 or x = -3

Question 2: Calculate the roots of the quadratic equation: x² - 4x + 1 = 0.

Answer: x = 2 ± √3

Question 3: Find the value(s) of x that satisfy: 3x² + 2x - 1 = 0.

Answer: x = ( -1/3 ) or x = 1

Question 4: Construct a quadratic equation with roots x = 3 and x = -2. Write the equation in standard form.

Answer: x² - x - 6 = 0

Question 5: Solve for x: 4x² + 4x + 1 = 0.

Answer: x = -1/2 (double root)

Question 6: A ball is thrown upwards and follows the path h(t) = -5t² + 10t + 2, where h(t) is height in meters and t in seconds. When will the ball hit the ground? (solve for t).

Answer: t = 0.4 or t = 1

Question 7: A rectangular garden's area is modeled by the equation A = x² + 6x, where x is the length of one side in meters. Find the value of x when the area is 35 m².

Answer: x = 1 or x = 5

Question 8: A car's stopping distance s (in meters) after applying brakes is given by s = 2t² + 3t, where t is the time in seconds. How long does it take the car to stop within 5 meters?

Answer: t ≈ 1.04 seconds

Question 9: If the quadratic equation 5x² - 7x + 2 = 0 has roots x₁ and x₂, find the sum and product of these roots.

Answer: Sum = 7/5, Product = 2/5

Question 10: Identify and correct the mistake: Solve x² + 4x + 5 = 0 using the quadratic formula, but mistakenly calculate the discriminant as 12 instead of 16.

Answer: Correct discriminant is 16, not 12. The roots are (-4 ± √16)/2, i.e., -2 and -2.