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
Mensuration
Coordinate Geometry
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
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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