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(x-1)(x+4)=0

2 min read Jun 17, 2024
(x-1)(x+4)=0

Solving the Equation (x-1)(x+4) = 0

This equation is a quadratic equation in factored form. We can use the Zero Product Property to solve it. This property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Here's how to solve it:

  1. Set each factor equal to zero:

    • x - 1 = 0
    • x + 4 = 0

  2. Solve for x in each equation:

    • x = 1
    • x = -4

Therefore, the solutions to the equation (x-1)(x+4) = 0 are x = 1 and x = -4.

Understanding the Solution

These solutions represent the x-values where the graph of the equation crosses the x-axis. The equation (x-1)(x+4) = 0 represents a parabola, and the points (1,0) and (-4,0) are the x-intercepts of the parabola.

Checking the Solution

We can check our solutions by substituting them back into the original equation:

  • For x = 1: (1 - 1)(1 + 4) = (0)(5) = 0
  • For x = -4: (-4 - 1)(-4 + 4) = (-5)(0) = 0

Since both solutions satisfy the original equation, we know they are correct.

In conclusion, solving the equation (x-1)(x+4) = 0 using the Zero Product Property gives us two solutions: x = 1 and x = -4. These solutions represent the x-intercepts of the parabola represented by the equation.

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