What is the sridharacharya method?

The Sridharacharya method, also known as the quadratic formula, is a mathematical technique used to find the roots of a quadratic equation. A quadratic equation is a polynomial equation of the form:

ax² + bx + c = 0,

where:

a, b, and c are constants, and a ≠ 0.
The roots of this equation can be calculated using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a).

Step-by-Step Explanation:
Identify the coefficients: From the given quadratic equation, identify the values of a, b, and c.

Calculate the discriminant: The discriminant (D) is given by: D = b² - 4ac.

If D > 0, the equation has two distinct real roots.
If D = 0, the equation has two equal real roots (repeated roots).
If D < 0, the equation has no real roots but two complex roots.
Apply the quadratic formula: Substitute the values of a, b, and c into the quadratic formula to find the roots: x₁ = (-b + √D) / (2a), x₂ = (-b - √D) / (2a).

Simplify the results: Perform the calculations to determine the exact values of x₁ and x₂.

Example:
Solve the quadratic equation: 2x² - 4x - 6 = 0.

Identify the coefficients: a = 2, b = -4, c = -6.

Calculate the discriminant: D = (-4)² - 4(2)(-6) = 16 + 48 = 64.

Apply the quadratic formula: x = [-(-4) ± √64] / (2 × 2) = [4 ± 8] / 4.

Simplify: x₁ = (4 + 8) / 4 = 12 / 4 = 3, x₂ = (4 - 8) / 4 = -4 / 4 = -1.

Final Answer:
The roots of the quadratic equation 2x² - 4x - 6 = 0 are x = 3 and x = -1.