Topics
Linear Equations in Two Variables
- Foundation of Linear Equations in Two Variables
- Simultaneous Linear Equations
- Graph of a Linear Equation in Two Variables
- Methods of Solving Linear Equations in Two Variables > Graphical Method
- Methods of Solving Linear Equations in Two Variables > Determinant method (Cramer’s Rule)
- Equations Reducible to Linear Equations
- Application of Simultaneous Equations
Quadratic Equations
- Concept of Quadratic Equations
- Factorisation Method
- Completing the Square Method
- Quadratic Formula (Shreedharacharya's Rule)
- Nature of Roots of a Quadratic Equation
- Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
- Formation of a Quadratic Equation with Given Roots
- Application of Quadratic Equation
Arithmetic Progression
Financial Planning
Probability
Statistics
Estimated time: 6 minutes
Maharashtra State Board: Class 10
Introduction
Equations are powerful tools for describing relationships between quantities. Among them, quadratic and cubic equations appear frequently in mathematics, physics, economics, engineering, and everyday problem-solving.
CBSE: Class 10
Maharashtra State Board: Class 10
Maharashtra State Board: Class 10
Formula: Relation Between Zeroes (Roots) and Coefficients
| Polynomial | Roots | Sum of roots | Pairwise product | Product of roots |
|
\[ax^2 + bx + c = 0\]
|
\[\alpha, \beta\]
|
\[-\frac{b}{a}\]
|
Not applicable
|
\[\frac{c}{a}\]
|
|
\[ax^3 + bx^2 + cx + d = 0\]
|
\[\alpha, \beta, \gamma\]
|
\[-\frac{b}{a}\]
|
\[\frac{c}{a}\]
|
\[-\frac{d}{a}\]
|
Maharashtra State Board: Class 10
Key Points: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
- For \[ ax^{2} + bx + c = 0: \]
\[ \alpha + \beta = -\frac{b}{a}, \qquad \alpha\beta = \frac{c}{a} \] - A quadratic with roots \[ \alpha, \beta \] is:
\[ x^{2} - (\alpha + \beta)x + \alpha\beta = 0 \] - For \[ ax^{3} + bx^{2} + cx + d = 0: \]
\[ \alpha + \beta + \gamma = -\frac{b}{a} \]
\[ \alpha\beta + \beta\gamma + \gamma\alpha = \frac{c}{a} \]
\[ \alpha\beta\gamma = -\frac{d}{a} \] - Always identify coefficients only after writing the equation in standard form.
Test Yourself
Video Tutorials
Shaalaa.com | Polynomials part 9 (Relation between zeroes & coefficient quadratic polynomials)
to track your progress
