(t-4)(3t+1)(t+2)=0

Jasonbradley

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Jun 16, 2024

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Solving the Cubic Equation: (t-4)(3t+1)(t+2)=0

This equation represents a cubic polynomial, meaning it has a highest power of 3. Solving for t involves finding the values that make the entire equation equal to zero.

Utilizing the Zero Product Property

The key to solving this equation is the Zero Product Property, which states: If the product of two or more factors is zero, then at least one of the factors must be zero.

In our case, we have three factors: (t-4), (3t+1), and (t+2). To make the entire equation equal to zero, at least one of these factors needs to be zero.

Finding the Solutions

Let's solve for t in each factor:

• (t-4) = 0

  • Adding 4 to both sides: t = 4

• (3t+1) = 0

  • Subtracting 1 from both sides: 3t = -1
  • Dividing both sides by 3: t = -1/3

• (t+2) = 0

  • Subtracting 2 from both sides: t = -2

Conclusion

Therefore, the solutions to the cubic equation (t-4)(3t+1)(t+2)=0 are:

• t = 4
• t = -1/3
• t = -2

These are the values of t that make the equation true. They represent the roots of the cubic polynomial.