Quadratic Equations — Class 10 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Quadratic Equations" — 9 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Quadratic Equations" — 9 important questions with detailed answers for CBSE board…
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Key Questions Covered:
- Define a quadratic equation and state the general form.
- Prove that the discriminant determines the nature of roots of a quadratic equ…
- Solve x² + 5x + 6 = 0 by factorisation.
- + 6 more questions in the full chapter
Solutions Summary:
| Question | Status |
|---|---|
| Define a quadratic equation and state the general form. | ✓ Solved |
| Prove that the discriminant determines the nature of root… | ✓ Solved |
| Solve x² + 5x + 6 = 0 by factorisation. | ✓ Solved |
Showing 3 of 9 questions
Q1: Define a quadratic equation and state the general form.
Quadratic Equation:
A quadratic equation in one variable is a polynomial equation of degree 2.
General form: ax² + bx + c = 0
where a, b, and c are real numbers and a ≠ 0.
The condition a ≠ 0 is essential because if a = 0, it becomes a linear equation, not quadratic.
Examples of quadratic equati...
Q2: Prove that the discriminant determines the nature of roots of a quadratic equation.
For the quadratic equation ax² + bx + c = 0, the discriminant is Δ = b² - 4ac.
The nature of roots is determined as follows:
1) If Δ > 0 (discriminant is positive):
- The equation has two distinct real roots
- Roots are given by x = (-b ± √Δ)/(2a)
- Example: x² + 5x + 6 = 0 has Δ = 25 ...
Q3: Solve x² + 5x + 6 = 0 by factorisation.
Given equation: x² + 5x + 6 = 0
Step 1: Identify factors
We need two numbers that multiply to 6 and add to 5.
Factors of 6 are: 1×6, 2×3
Checking: 2 + 3 = 5 ✓ and 2 × 3 = 6 ✓
Step 2: Factorise
x² + 5x + 6 = (x + 2)(x + 3) = 0
Step 3: Apply zero product property
Either (x + 2) = 0 or (x + 3) = 0
T...
Showing 3 of 9 questions. Visit the full page for complete solutions.