Class 10 Maths — Chapter 2: POLYNOMIALS

What you'll learn

• ▸Definition and Degree of Polynomials
• ▸Value and Zeroes of a Polynomial
• ▸Geometrical Meaning of Zeroes
• ▸Number of Zeroes from a Graph
• ▸Relationship between Zeroes and Coefficients (Quadratic)
• ▸Forming a Quadratic Polynomial
• ▸Division Algorithm for Polynomials

Chapter Summary

--- PAGE 1 --- 1062CH02 POLYNOMIALS 2 2.1 Introduction In Class IX, you have studied polynomials in one variable and their degrees. Recall that if p(x) is a polynomial in x, the highest power of x in p(x) is called the degree of the polynomial p(x). For example, 4x + 2 is a polynomial in the variable x of degree 1, 2y² – 3y + 4 is a polynomial in the variable y of degree 2, 5x³ – 4x² + x – √2 is a polynomial in the variable x of degree 3 and 7u⁶ – ³⁄₂ u⁴ + 4u² + u – 8 is a polynomial in the variable u of degree 6. Expressions like ¹⁄ₓ₋₁, √x+2, ¹⁄ₓ²⁺²ˣ⁺³ etc., are not polynomials. A polynomial of degree 1 is called a linear polynomial. For example, 2x – 3, √3x + 5, y + √2, x – ²⁄₁₁, 3z + 4, ²⁄₃u + 1, etc., are all linear polynomials. Polynomials such as 2x + 5 – x², x³ + 1, etc., are not linear polynomials. A polynomial of degree 2 is called a quadratic polynomial. The name ‘quadratic’ has been derived from the word ‘quadrate’, which means ‘square’. 2x² + 3x – ²⁄₅, y² – 2, 2 – x² + …

Practice Questions from this Chapter

Tap "Get Solution" on any question to ask our AI tutor.

1. Discover everyday uses for polynomial zeroes. Get Solution →
2. Visualize quadratic graphs with a simulation. Get Solution →
3. Calculate polynomial values quickly using a trick. Get Solution →
4. What is a polynomial of degree 1 called? Get Solution →
5. What is the degree of the polynomial 2y² – 3y + 4? Get Solution →
6. A polynomial of degree 3 is called a what? Get Solution →
7. According to the text, a real number k is a zero of a polynomial p(x) if which condition is met? Get Solution →
8. What is the general form of a quadratic polynomial in the variable x? Get Solution →

Did you know?

• 💡 Polynomials help cartoon animators create fluid, lifelike movements.
• 💡 The shape of a satellite dish is a parabola, focusing signals perfectly.
• 💡 Ancient Greeks studied parabolas by slicing cones in specific ways.
• 💡 Mathematicians use polynomials to decode secret messages in cryptography.
• 💡 A polynomial's "degree" in math originally referred to steps in a calculation.

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