ROOTS OF A QUADRATIC EQUATION
Definition Of Roots Of A Quadratic Equation
The solutions of a quadratic equation are called the roots of a quadratic equation.
Example on Roots of a Quadratic Equation
The solutions or the roots of the quadratic equation x2 - x - 2 are 2 and - 1.
Video Examples: Roots of a Quadratic Equation
Solved Example on Roots of a Quadratic Equation
Ques: The graph represents the equation x2 - x - 6. Find the roots of the quadratic equation x2 - x - 6.
Choices:
A. x = 3, x = 2
B. x = 3, x = - 2
C. x = - 6
D. x = - 6, x = 3, x = - 2
Correct Answer: B
Solution:
Step 1: The roots of the quadratic equation x2 - x - 6 are 3 and - 2.
Quick Summary
- Roots are the x-values where the quadratic equation equals zero.
- Roots can be found by factoring, using the quadratic formula, or graphing.
- A quadratic equation can have two real roots, one real root (a repeated root), or two complex roots.
🍎 Teacher Insights
Emphasize the connection between the roots and the x-intercepts of the graph. Use visual aids like graphs to illustrate the concept. Provide ample practice problems covering different methods of finding roots.🎓 Prerequisites
- Algebra
- Factoring
- Solving Equations
Check Your Knowledge
Q1: What are the roots of the equation x^2 - x - 6 = 0?
Q2: How many real roots does the quadratic equation x^2 + 1 = 0 have?
Frequently Asked Questions
Q: What is the difference between roots and solutions?
A: In the context of quadratic equations, the terms 'roots' and 'solutions' are interchangeable.
Q: Can a quadratic equation have no real roots?
A: Yes, if the discriminant (b^2 - 4ac) is negative, the quadratic equation has two complex roots and no real roots.