EQUAÇÃO DO 2 GRAU FÓRMULA DE BHÁSKARA  \Prof. Gis/ AULA 2
Table of Contents
Introduction
This tutorial will guide you through solving a seconddegree equation using Bhaskara's formula, as presented by Prof. Gis. Understanding how to work with seconddegree equations is crucial in algebra, as they frequently appear in various mathematical contexts.
Step 1: Understanding the SecondDegree Equation
A seconddegree equation is expressed in the standard form:
ax² + bx + c = 0
 a: Coefficient of x² (cannot be zero)
 b: Coefficient of x
 c: Constant term
Classification
 Complete Equation: All coefficients (a, b, c) are present.
 Incomplete Equation: One or more coefficients are missing (b or c can be zero).
Note: If a = 0, it is no longer a seconddegree equation but a firstdegree one.
Step 2: Identifying Coefficients
To solve an equation, first identify the coefficients:
 Look at the equation and assign values to a, b, and c.
 Example: For the equation 2x² + 3x  5 = 0:
 a = 2
 b = 3
 c = 5
Step 3: Applying Bhaskara's Formula
Bhaskara's formula is used to find the roots of the seconddegree equation:
x = (b ± √(b²  4ac)) / (2a)
Steps to Use the Formula

Calculate the Discriminant:
 Discriminant (D) = b²  4ac
 Example: For a = 2, b = 3, c = 5:
 D = (3)²  4 * (2) * (5) = 9 + 40 = 49

Determine Roots:
 If D > 0: Two distinct real roots
 If D = 0: One real root (repeated)
 If D < 0: No real roots (complex roots)

Substitute into Bhaskara's Formula:
 Use the calculated D to find x:
 Example: Continuing from the above:
 Since D = 49 (which is greater than 0):
 x = (3 ± √49) / (2 * 2)
 x = (3 ± 7) / 4

Simplify the Results:
 First root:
 x₁ = (3 + 7) / 4 = 4 / 4 = 1
 Second root:
 x₂ = (3  7) / 4 = 10 / 4 = 2.5
 First root:
Step 4: Solving Incomplete Equations
For incomplete equations, such as ax² + c = 0 or ax² + bx = 0, you can still apply similar methods:
 If c = 0, factor the equation or use simple algebraic manipulation.
 If b = 0, the equation simplifies to ax² + c = 0, and you can isolate x².
Example of Incomplete Equation
For the equation 2x²  8 = 0:
 Isolate x²: 2x² = 8
 Divide by 2: x² = 4
 Take the square root: x = ±2
Conclusion
You've learned how to solve seconddegree equations using Bhaskara's formula and how to classify equations as complete or incomplete. Remember to identify coefficients correctly and calculate the discriminant to determine the nature of the roots. For further practice, consider solving additional equations or exploring related topics in algebra.