Topics
Real Numbers
Number Systems
Algebra
Polynomials
Coordinate Geometry
Pair of Linear Equations in Two Variables
- Pair of Linear Equations in Two Variables
- Graphical Method with Different Cases of Solution
- Algebraic Methods of Solving a Pair of Linear Equations
- Substitution Method
- Elimination Method
Geometry
Quadratic Equations
Trigonometry
Arithmetic Progressions
Mensuration
Coordinate Geometry
Statistics and Probability
Triangles
Circles
Introduction to Trigonometry
Heights and Distances
- Angles of Elevation and Depression
- Problems based on Elevation and Depression
Areas Related to Circles
Surface Areas and Volumes
Statistics
Probability
CBSE: Class 10
Definition: Geometrical Meaning of Zeroes
The zeroes of a polynomial are the x-coordinates of the points where the graph of y = p(x) intersects the x-axis.
CBSE: Class 10
Key Points: Geometrical Meaning of the Zeroes of a Polynomial
A quadratic polynomial can have only:
Case (i): Two zeroes
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Graph cuts the x-axis at two distinct points
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Two distinct real zeroes
Case (ii): One zero
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Graph touches the x-axis at exactly one point
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One real (repeated) zero
Case (iii): No zero
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The graph does not touch the x-axis at all
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No real zero
A polynomial of degree n can have at most n zeroes.
Video Tutorials
Shaalaa.com | Polynomials part 3 (Zeroes of polynomials)
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