Jasonbradley
Home

(3x+1)2(x+7)(x-2)4=0

2 min read Jun 16, 2024
(3x+1)2(x+7)(x-2)4=0

Solving the Equation: (3x+1)^2(x+7)(x-2)^4 = 0

This equation involves a product of multiple factors equaling zero. To find the solutions, we can utilize the Zero Product Property, which states that if the product of multiple factors is zero, then at least one of the factors must be zero.

Let's break down the equation and find the solutions:

  1. Identify the factors:

    • (3x + 1)^2
    • (x + 7)
    • (x - 2)^4

  2. Set each factor equal to zero:

    • (3x + 1)^2 = 0
    • (x + 7) = 0
    • (x - 2)^4 = 0

  3. Solve for x in each equation:

    • (3x + 1)^2 = 0

      • Take the square root of both sides: 3x + 1 = 0
      • Subtract 1 from both sides: 3x = -1
      • Divide both sides by 3: x = -1/3

    • (x + 7) = 0

      • Subtract 7 from both sides: x = -7

    • (x - 2)^4 = 0

      • Take the fourth root of both sides: x - 2 = 0
      • Add 2 to both sides: x = 2

Therefore, the solutions to the equation (3x+1)^2(x+7)(x-2)^4 = 0 are:

  • x = -1/3
  • x = -7
  • x = 2

Important Note: The solution x = 2 appears with a multiplicity of 4 due to the factor (x-2)^4. This means that the solution x = 2 is repeated four times.

Related Post

Featured Posts