Topics
Number Systems
Number Systems
Algebra
Polynomials
Linear Equations in Two Variables
Algebraic Expressions
Algebraic Identities
Coordinate Geometry
Geometry
Introduction to Euclid’S Geometry
Lines and Angles
Triangles
Quadrilaterals
- Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
- Angle Sum Property of a Quadrilateral
- Types of Quadrilaterals
- Another Condition for a Quadrilateral to Be a Parallelogram
- Theorem of Midpoints of Two Sides of a Triangle
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- Theorem : If Each Pair of Opposite Sides of a Quadrilateral is Equal, Then It is a Parallelogram.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Theorem : If the Diagonals of a Quadrilateral Bisect Each Other, Then It is a Parallelogram
Area
Circles
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Angle Subtended by a Chord at a Point
- Perpendicular from the Centre to a Chord
- Circles Passing Through One, Two, Three Points
- Equal Chords and Their Distances from the Centre
- Angle Subtended by an Arc of a Circle
- Cyclic Quadrilateral
Constructions
Mensuration
Areas - Heron’S Formula
Surface Areas and Volumes
Statistics and Probability
Statistics
Probability
notes
Consider the polynomial `p(x) = 5x^3 – 2x^2 + 3x – 2`.
If we replace x by 1 everywhere in p(x), we get
`p(1) = 5 × (1)^3 – 2 × (1)^2 + 3 × (1) – 2`
= 5 – 2 + 3 –2
= 4
So, we say that the value of p(x) at x = 1 is 4.
Similarly, the polynomial p(x) = x – 1.
p(1) = 1 – 1 = 0. As p(1) = 0, we say that 1 is a zero of the polynomial p(x).
A non-zero constant polynomial has no zero. Every real number is a zero of the zero polynomial.
If you would like to contribute notes or other learning material, please submit them using the button below.
Shaalaa.com | Zeroes of a Polynomial
to track your progress
Related QuestionsVIEW ALL [17]
Advertisement Remove all ads