Solving Quadratic Equations with Bhaskara's Formula

Understanding the Bhaskara Formula

• Often perceived as complicated, but it's quite straightforward with proper explanation.

Components of a Quadratic Equation

• Coefficients a, b, and c:
  • a: Coefficient next to x².
  • b: Coefficient next to x.
  • c: Constant term in the equation.

Calculating the Discriminant (Delta, Δ)

• Formula: Δ = b² - 4ac
  • Δ (Discriminant): Determines the nature of the roots of the quadratic equation.
  • Remember: 4 is a constant value in the formula.

Steps to Solve Using Bhaskara's Formula

1. Identify Coefficients from the equation.
2. Calculate Δ (Discriminant) using the formula Δ = b² - 4ac.
3. Solve for x: Use the formula x = (-b ± √Δ) / (2*a).
   • This formula yields two possible values for x, known as the roots.

Example Explained

• Given equation coefficients: a = 4, b = -3, c = -1.
• Calculation of Δ: Using the given values, Δ turns out to be 25.
• Solving for x: With Δ = 25, substitute the values into the formula to find the two possible values for x.

Finding the Roots

• Once Δ is known, the roots of the equation can be calculated as:
  • x₁ = (3 + √25) / 8
  • x₂ = (3 - √25) / 8
  • These calculations yield two roots, one being a whole number and the other a fraction.

Verification

• To verify the roots, substitute them back into the original equation and ensure it simplifies to 0.

Conclusion

• The process de-mystifies the Bhaskara formula and demonstrates that solving quadratic equations this way is not as daunting as it may seem.
• The exercise serves as valuable practice for solving complete quadratic equations.

Tips for Success

• Pay attention to the signs of the coefficients.
• Follow operation order: power first, then multiplication/division, and addition/subtraction last.
• Always verify your solutions by substituting the roots back into the original equation.