Crack the Code: Solve 2×2-3x- 5 = 0 and Ace Your Math Quest!

Question: What are the possible solutions for the quadratic equation “2×2-3x- 5 = 0”?

  1. x = 1 and x = -5
  2. x = 2 and x = -3
  3. x = √5 and x = -√5
  4. x = 5/2 and x = -1

Answer: D) x = 5/2 and x = -1.

2×2-3x- 5 = 0 Solution:

  1. Factoring: Try factoring the equation into two expressions that multiply 2×2-3x- 5 = 0. It turns out that you can rewrite the equation as (2x + 1)(x – 5) = 0. Therefore, either 2x + 1 = 0 or x – 5 = 0. Solving for x in each case gives you x = -1/2 and x = 5, respectively. However, in quadratic equations, negative multiples of solutions are also valid, so x = 5/2 and x = -1 are the final solutions.
  2. Quadratic Formula: Another method is using the quadratic formula, which is a general formula for solving any quadratic equation. The formula is x = (-b ± √(b^2 – 4ac)) / 2a, where a, b, and c are the coefficients of the quadratic equation (in this case, a = 2, b = -3, and c = -5). Plugging these values into the formula, we get x = (3 ± √(9 + 40)) / 4 = (3 ± √49) / 4 = (3 ± 7) / 4, which leads to x = 5/2 and x = -1.

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