BHASKARA FORMULA: Exercise 12.4

The Bhaskara formula, also known as the quadratic formula, is a mathematical formula that is used to solve quadratic equations of the ax² + bx + c = 0 form, where A, B and C are constant.

Bhaskara formula

Bhaskara's formula is:

x = (-b ± √ (b² - 4ac)) / 2a

Where:

- X is the solution of the equation
- A is the coefficient of x²
- B is the coefficient of x
- C is the constant term
- √ It is the square root symbol

History

Bhaskara's formula was discovered by Indian mathematician Bhaskara in the twelfth century. However, the formula was also discovered independently by other mathematicians, such as Greek Euclid and Persian al-Khwarizmi.

Example

Suppose we want to solve the equation x² + 5x + 6 = 0. Using the Bhaskara formula, we get:

x = (-5 ± √ (5² - 4 (1) (6))) / 2 (1)
x = (-5 ± √ (25 - 24)) / 2
x = (-5 ± √1) / 2
x = (-5 ± 1) / 2

Therefore, the solutions of the equation are x = -2 and x = -3.

Importance

The Bhaskara formula is a fundamental tool in algebra and is used in a wide variety of applications, such as the resolution of quadratic equations, polynomial factorization and the resolution of optimization problems.