Solve the quadratic equation 4x ^ 2 – 5x – 12 = 0

Question: Which of the following is the correct solution to the quadratic equation 4x ^ 2 – 5x – 12 = 0?

  1. x = 5/8 + i√167/8
  2. x = 5/8 – i√167/8
  3. x = -3/8 + i√167/8
  4. x = -3/8 – i√167/8

Answer: A) x = 5/8 + i√167/8

Solution:

We can solve the quadratic equation 4x^2 - 5x - 12 = 0 using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 4, b = -5, and c = -12. Substituting these values into the quadratic formula, we get:

x = (-(-5) ± √((-5)² - 4 * 4 * -12)) / 2 * 4
x = (5 ± √(225 + 192)) / 8
x = (5 ± √417) / 8
x = 5/8 ± i√167/8

4x ^ 2 - 5x - 12 = 0
Quadratic Formula

Therefore, the correct solution to the quadratic equation 4x^2 - 5x - 12 = 0 is x = 5/8 + i√167/8.

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