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
- Concept of Polyomial
- Graph of Polynomials
- Geometrical Meaning of the Zeroes of a Polynomial
- Relation Between Zeroes (Roots) and Coefficients of a Polynomial
- Relationship Between the Zeros and Coefficients of a Quadratic Polynomial
- Relationship between Zeros And Coefficients of a Cubic Polynomial
- Division Algorithm for 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 |
|
\[ax^2 + bx + c = 0\]
|
\[\alpha, \beta\]
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\[-\frac{b}{a}\]
|
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
