Quadratic Equations Class 10 Mathematics — Revision Notes
This chapter explores quadratic equations of the form ax^2 + bx + c = 0. Students learn solution methods including factorization and quadratic formula, and
TL;DR: This chapter explores quadratic equations of the form ax^2 + bx + c = 0. Students learn solution methods including factorization and quadratic formula…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
This chapter explores quadratic equations of the form ax^2 + bx + c = 0. Students learn solution methods including factorization and quadratic formula, and
Quadratic Equation Basics
- Standard form: ax^2 + bx + c = 0 where a ≠ 0
- Degree is 2, having at most 2 real roots
- If b = 0: ax^2 + c = 0 called pure quadratic
- If c = 0: ax^2 + bx = 0 called incomplete quadratic
Solution by Factorization
- Factorize ax^2 + bx + c into product of linear factors
- Set each factor equal to zero and solve
- Works when roots are rational and can be easily found
- Example: x^2 - 5x + 6 = 0 becomes (x-2)(x-3) = 0, so x = 2 or 3
Quadratic Formula
- For ax^2 + bx + c = 0: x = (-b ± sqrt(b^2 - 4ac)) / 2a
- Discriminant D = b^2 - 4ac determines nature of roots
- D > 0: two distinct real roots
- D = 0: two equal real roots
- D < 0: no real roots (two complex roots)
Applications
- Speed and distance problems: set up quadratic from given conditions
- Geometry problems: area, perimeter conditions lead to quadratic
- Ages and work problems converted to quadratic equations
- Check that roots are valid for given problem context
Key Terms
- Quadratic Equation: Polynomial equation of degree 2 in the form ax^2 + bx + c = 0
- Discriminant: Value b^2 - 4ac determining nature of roots of quadratic
- Roots: Values of variable satisfying the quadratic equation
Frequently Asked Questions
When do quadratic equations have no real roots?
When discriminant D = b^2 - 4ac < 0. In this case, roots are complex (involve imaginary unit i).
How do you solve x^2 - 4x + 3 = 0?
By factorization: (x-1)(x-3) = 0, so x = 1 or 3. Or using formula: x = (4 ± sqrt(16-12))/2 = (4 ± 2)/2, giving x = 3 or 1.
More Class 10 Mathematics Revision Notes
- Real Numbers
- Polynomials
- Pair of Linear Equations in Two Variables
- Arithmetic Progressions
- Triangles
- Coordinate Geometry
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