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What is the solution to the equation 2x^2 - 4x - 6 = 0 using the quadratic formu

Practice Questions

Q1
What is the solution to the equation 2x^2 - 4x - 6 = 0 using the quadratic formula?
  1. x = 3
  2. x = -1
  3. x = 2
  4. x = -3

Questions & Step-by-Step Solutions

What is the solution to the equation 2x^2 - 4x - 6 = 0 using the quadratic formula?
  • Step 1: Identify the coefficients in the equation 2x^2 - 4x - 6 = 0. Here, a = 2, b = -4, and c = -6.
  • Step 2: Write down the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a.
  • Step 3: Calculate the discriminant (b² - 4ac). First, find b²: (-4)² = 16.
  • Step 4: Calculate 4ac: 4 * 2 * -6 = -48. So, 16 - (-48) = 16 + 48 = 64.
  • Step 5: Substitute the values into the quadratic formula: x = (4 ± √64) / 4.
  • Step 6: Calculate √64, which is 8. So, x = (4 ± 8) / 4.
  • Step 7: Solve for the two possible values of x: First, x = (4 + 8) / 4 = 12 / 4 = 3. Second, x = (4 - 8) / 4 = -4 / 4 = -1.
  • Step 8: The solutions to the equation are x = 3 and x = -1.
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