(2x-1)(x-5)(x+2)=0

Jasonbradley

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Jun 16, 2024

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Solving the Cubic Equation: (2x-1)(x-5)(x+2) = 0

This equation represents a cubic function, meaning it has a highest power of 3. To solve for the values of x that satisfy this equation, we can utilize the Zero Product Property.

This property states that if the product of multiple factors is equal to zero, then at least one of those factors must be equal to zero.

Applying the Zero Product Property

Let's break down our equation:

• (2x - 1)(x - 5)(x + 2) = 0

We have three factors: (2x - 1), (x - 5), and (x + 2).

For the product to be zero, at least one of these factors must be zero. Let's set each factor equal to zero and solve for x:

1. 2x - 1 = 0

   • Add 1 to both sides: 2x = 1
   • Divide both sides by 2: x = 1/2

2. x - 5 = 0

   • Add 5 to both sides: x = 5

3. x + 2 = 0

   • Subtract 2 from both sides: x = -2

Solutions

Therefore, the solutions to the equation (2x-1)(x-5)(x+2) = 0 are:

• x = 1/2
• x = 5
• x = -2

These are the roots of the cubic equation, representing the points where the graph of the function intersects the x-axis.