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(x-6)(x+1)=0 Formula

2 min read Jun 17, 2024
(x-6)(x+1)=0 Formula

Solving Quadratic Equations using the Zero Product Property

The equation (x - 6)(x + 1) = 0 is a quadratic equation in factored form. To solve for the values of x that satisfy the equation, we can use the Zero Product Property.

The Zero Product Property

The Zero Product Property states that if the product of two or more factors is equal to zero, then at least one of the factors must be zero.

Applying the Zero Product Property to Solve the Equation

  1. Identify the factors: In the equation (x - 6)(x + 1) = 0, we have two factors: (x - 6) and (x + 1).

  2. Set each factor equal to zero:

    • x - 6 = 0
    • x + 1 = 0

  3. Solve for x in each equation:

    • x = 6
    • x = -1

Conclusion

Therefore, the solutions to the equation (x - 6)(x + 1) = 0 are x = 6 and x = -1. These values of x make the product of the two factors equal to zero, satisfying the equation.

Note: The Zero Product Property is a powerful tool for solving quadratic equations that are already in factored form. It allows us to quickly find the solutions without the need for complex algebraic manipulations.

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