Topics
Goods and Services Tax (G.S.T.)
Commercial Mathematics
Compound Interest
- Compound Interest as a Repeated Simple Interest Computation with a Growing Principal
- Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years
- Use of Formula
- Finding CI from the Relation CI = A – P
Banking
Algebra
Shares and Dividends
Geometry
Mensuration
Linear Inequations
Trigonometry
Quadratic Equations
- Quadratic Equations
- Method of Solving a Quadratic Equation
- Factorisation Method
- Quadratic Formula (Shreedharacharya's Rule)
- Nature of Roots of a Quadratic Equation
- Equations Reducible to Quadratic Equations
Statistics
Ratio and Proportion
Probability
Factorisation of Polynomials
- Function and Polynomial
- Division Algorithm for Polynomials
- Remainder Theorem
- Factor Theorem
- Applications of Factor Theorem
Matrices
Arithmetic and Geometric Progression
Co-ordinate Geometry
- Co-ordinate Geometry
- Advanced Concept of Reflection in Mathematics
- Invariant Points
- Combination of Reflections
- Using Graph Paper for Reflection
Symmetry
Similarity
Loci
- Locus
- Points Equidistant from Two Given Points
- Points Equidistant from Two Intersecting Lines
- Summary of Important Results on Locus
- Important Points on Concurrency in a Triangle
Circles
Tangent and Secant Properties
Constructions
Area and Volume of Solids (Cylinder, Cone and Sphere)
- Mensuration of Cylinder
- Hollow Cylinder
- Mensuration of Cones
- Mensuration of a Sphere
- Hemisphere
- Conversion of Solids
- Solid Figures
- Problems on Mensuration
Trigonometrical Identities
Heights and Distances
- Angles of Elevation and Depression
- Problems based on Elevation and Depression
Statistics : basic concepts, Mean, Median, Mode. Histograms and Ogive
Probability
- Definition: Quadratic Equation
- Definition: Roots of a Quadratic Equation
- Types of Quadratic Equations
- Definition: Solution Set
- Examples
Maharashtra State Board: Class 10
CISCE: Class 10
Definition: Quadratic Equations
An equation with one variable, in which the highest power of the variable is two, is known as a quadratic equation.
Standard Form:
ax2 + bx + c = 0, a ≠ 0
For example :
(i) 3x2 + 4x + 7 = 0
(ii) 4x2 + 5x = 0
Maharashtra State Board: Class 10
CISCE: Class 10
Definition: Roots of a Quadratic Equation
A value of the variable which satisfies the equation is called a root (solution).
If substituting a value of x makes the polynomial zero, that value is a root.
- A number α is called a root of ax2 + bx + c = 0, if aα2 + bα + c = 0
CISCE: Class 10
Definition: Solution Set
The set of elements representing the roots of a quadratic equation is called its solution set.
Definition: Adjected Quadratic Equation
If a quadratic equation contains only two terms where one is a square term and the other is the first power term of the unknown, it is called adjected quadratic equation.
For example :
(i) 4x2 + 5x = 0
(ii) 7x2 − 3x = 0, etc.
Definition: Pure Quadratic Equation
If the quadratic equation contains only the square of the unknown, it is called a pure quadratic equation.
For example :
(i) x2 = 4
(ii) 3x2 − 8 = 0, etc.
