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0=(2y−1)(8−y)

2 min read Jun 17, 2024
0=(2y−1)(8−y)

Solving the Equation: 0 = (2y - 1)(8 - y)

This equation represents a quadratic equation in factored form. To solve for y, we can utilize the Zero Product Property. This property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Steps:

  1. Set each factor equal to zero.

    • 2y - 1 = 0
    • 8 - y = 0

  2. Solve each equation for y.

    • 2y = 1
    • y = 1/2
    • y = 8

Therefore, the solutions to the equation 0 = (2y - 1)(8 - y) are y = 1/2 and y = 8.

Explanation:

  • When y = 1/2, the first factor (2y - 1) becomes zero, making the entire product zero.
  • When y = 8, the second factor (8 - y) becomes zero, again resulting in the product being zero.

Graphical Representation:

This equation can be represented graphically as a parabola intersecting the x-axis at the points (1/2, 0) and (8, 0). The x-intercepts of the graph correspond to the solutions of the equation.

In summary, understanding the Zero Product Property allows us to easily solve factored quadratic equations. By setting each factor equal to zero, we can determine the values of the variable that make the entire equation true.

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