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

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

Solving the Cubic Equation: (x-4)(x+2)(x-1) = 0

This equation represents a cubic function set equal to zero. To find the solutions, we need to determine the values of x that make the equation true.

The Zero Product Property

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

Solving for x

Applying the Zero Product Property to our equation:

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

This means one or more of the following must be true:

  • x - 4 = 0
  • x + 2 = 0
  • x - 1 = 0

Solving each of these linear equations:

  • x = 4
  • x = -2
  • x = 1

Conclusion

Therefore, the solutions to the cubic equation (x-4)(x+2)(x-1) = 0 are x = 4, x = -2, and x = 1. These are the roots or zeros of the equation.

This method of solving cubic equations by factoring is particularly useful when the equation is already presented in factored form. It allows us to quickly identify the solutions without the need for more complex algebraic manipulation.

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