Topics
Real Numbers
- Concept of Divisibility
- Euclid's Division Lemma
- Euclid’s Division Algorithm
- Application of Euclid Lemma > Finding the HCF of Two Positive Integers
- Application of Euclid Lemma > Finding the HCF of Three Numbers
- Application of Euclid Lemma > On Expressing the HCF of Two Numbers a and b in the Form xa + yb
- Fundamental Theorem of Arithmetic
- Applications of the Fundamental Theorem of Arithmetic
- Rational Numbers
- Irrational Numbers
- Nature of the Decimal Expansions of Rational Numbers
Number Systems
Algebra
Polynomials
Coordinate Geometry
Pair of Linear Equations in Two Variables
Quadratic Equations
Geometry
Arithmetic Progressions
Trignometry
Coordinate Geometry
Mensuration
Statistics and Probability
Triangles
Circles
- Tangent to a Circle
- Number of Tangents from a Point on a Circle
Introduction to Trigonometry
Some Applications of Trigonometry
- Angles of Elevation and Depression
- Problems based on Elevation and Depression
Areas Related to Circles
Surface Areas and Volumes
Statistics
Probability
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
