Polynomials — Class 10 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Polynomials" — 9 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Polynomials" — 9 important questions with detailed answers for CBSE board exam pre…
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Key Questions Covered:
- State the relationship between zeroes and coefficients of a quadratic polynom…
- Define a polynomial. What do you mean by the degree of a polynomial?
- Divide p(x) = x³ + 3x² + 3x + 1 by g(x) = x + 1 using long division.
- + 6 more questions in the full chapter
Solutions Summary:
| Question | Status |
|---|---|
| State the relationship between zeroes and coefficients of… | ✓ Solved |
| Define a polynomial. What do you mean by the degree of a … | ✓ Solved |
| Divide p(x) = x³ + 3x² + 3x + 1 by g(x) = x + 1 using lon… | ✓ Solved |
Showing 3 of 9 questions
Q1: State the relationship between zeroes and coefficients of a quadratic polynomial ax² + bx + c.
For a quadratic polynomial ax² + bx + c with zeroes α and β:
Sum of zeroes: α + β = -b/a
Product of zeroes: α × β = c/a
Example: For the polynomial 2x² - 5x + 3, with a = 2, b = -5, c = 3:
If the zeroes are α and β, then:
α + β = -(-5)/2 = 5/2
α × β = 3/2
We can verify: zeroes are 1 and 3/2
1 + ...
Q2: Define a polynomial. What do you mean by the degree of a polynomial?
Polynomial:
A polynomial is an algebraic expression consisting of terms with variables and coefficients, where variables have non-negative integer powers.
General form: p(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀
where aₙ, aₙ₋₁, ..., a₁, a₀ are constants and n is a non-negative integer.
Degree of a po...
Q3: Divide p(x) = x³ + 3x² + 3x + 1 by g(x) = x + 1 using long division.
Polynomial long division of (x³ + 3x² + 3x + 1) ÷ (x + 1):
Step 1: Divide first term of dividend by first term of divisor
x³ ÷ x = x²
Multiply: x²(x + 1) = x³ + x²
Subtract: (x³ + 3x² + 3x + 1) - (x³ + x²) = 2x² + 3x + 1
Step 2: Repeat with new dividend 2x² + 3x + 1
2x² ÷ x = 2x
Multiply: 2x(x + 1...
Showing 3 of 9 questions. Visit the full page for complete solutions.