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

2 min read Jun 17, 2024

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

This equation represents a simple quadratic equation in factored form. To solve for the values of x that satisfy the equation, we can utilize the Zero Product Property.

The Zero Product Property

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

In our equation, (x-1) and (x-4) are the two factors. Therefore, to make the product equal to zero, either:

x - 1 = 0 or
x - 4 = 0

Solving for x

Now we solve each equation separately:

x - 1 = 0 Adding 1 to both sides, we get: x = 1
x - 4 = 0 Adding 4 to both sides, we get: x = 4

The Solutions

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

Graphical Representation

The equation (x-1)(x-4) = 0 represents a parabola that intersects the x-axis at the points x = 1 and x = 4. This visually confirms that these are the solutions to the equation.

Conclusion

By applying the Zero Product Property, we successfully solved the equation (x-1)(x-4) = 0 and found the solutions x = 1 and x = 4. This method is a fundamental tool in solving quadratic equations, especially when they are presented in factored form.