QUADRATIC EQUATION
Definition Of Quadratic Equation
A Quadratic Equation is one that can be written in the standard form ax2 + bx + c = 0, where a, b, and c are real numbers and a does not equal zero.
More About Quadratic Equation
In any quadratic equation, the highest power of an unknown quantity is 2.
A quadratic equation can contain one or more second power variables.
A quadratic equation has at most two solutions.
The graph of a quadratic equation is a parabola.
Video Examples: Introduction to the quadratic equation
Example of Quadratic Equation
7x2 + 9x + 2 = 0 is a quadratic equation, because this equation is in the form ax2 + bx + c = 0, where a = 7, b = 9, and c = 2 and the variable is a second degree variable.
Solved Example on Quadratic Equation
Ques: Which of the following is a quadratic equation?
Choices:
A. x2 + 5x + 1 = 0
B. (3x - 1) (2x + 1) (x + 3) = 0
C. x + 
= x2
D. x (x2 - 1) - 4x + 28 = 0
Correct Answer: A
Solution:
Step 1: A quadratic equation can be expressed in the form ax2 + bx + c = 0.
Step 2: Here, the only equation that has a second degree variable is x2 + 5x + 1 = 0 and all other equations have third degree variables.
Step 3: So, the quadratic equation is x2 + 5x + 1 = 0.
Quick Summary
- A quadratic equation has a highest power of 2 for the unknown variable.
- It can have one or more second power variables.
- A quadratic equation has at most two solutions (roots).
- The graph of a quadratic equation is a parabola.
🍎 Teacher Insights
Emphasize the importance of understanding the standard form. Use visual aids like graphs of parabolas to illustrate the solutions. Encourage students to check their solutions by substituting them back into the original equation.🎓 Prerequisites
- Basic Algebra
- Solving Linear Equations
- Understanding Variables and Coefficients
Check Your Knowledge
Q1: Which of the following is a quadratic equation?
Q2: What is the value of 'a' in the quadratic equation 3x² - 5x + 2 = 0?
Frequently Asked Questions
Q: What is the standard form of a quadratic equation?
A: The standard form is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
Q: How many solutions can a quadratic equation have?
A: A quadratic equation can have zero, one, or two real solutions.