सहज रुपमा सिक्न प्रयास गर्नुहोस्।
Equation
CDC Grade 10 • वर्ग समीकरण
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Namaste & Welcome! Let’s explore Quadratic Equations.
Explore interactive algebra coordinates, dynamic CDC-style exams, visual coefficient grids, and get helpful chimes as you master Compulsory Mathematics.
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CDC Class 10 Syllabus Progress
Dynamic Achievements
Nepal Class 10 CDC Quadratic Curriculum Guide
SEC 1 General Equation standard definitions
English Outline
An equation of degree 2 containing a single variable is called a **Quadratic Equation**. Its standard or general form is written as:
Where $a, b,$ and $c$ are real numbers, and $a \neq 0$.
नेपाली अनुवाद
दोस्रो घात भएको र एउटा मात्र चल राशि भएको समीकरणलाई **वर्ग समीकरण (Quadratic Equation)** भनिन्छ। यसको प्रमाणिक रूप यस प्रकार छ:
जहाँ $a, b$ र $c$ वास्तविक संख्याहरू हुन् र $a \neq 0$ हुनुपर्छ।
SEC 2 Discriminant and Character of Roots
The discriminant controls the visual x-intercept intersections. Its algebraic formula is:
1. $D > 0$
Roots are real and unequal (वास्तविक र फरक)
2. $D = 0$
Roots are real and equal (वास्तविक र बराबर)
3. $D < 0$
Roots are imaginary (काल्पनिक)
CDC Syllabus Insights
Common Mistake #1
Do not identify coefficients without moving terms into the strict form $ax^2 + bx + c = 0$. Watch your signs!
Common Mistake #2
When calculating $-b$ with $b = -3$, remember that $-b = -(-3) = +3$.
Formula Reference List
Standard Quadratic Form
$$ax^2 + bx + c = 0$$
Quadratic Formula (Sridhar Acharya)
$$x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}$$
Vertex Coordinate Pairs
$$\left( -\frac{b}{2a}, \frac{4ac-b^2}{4a} \right)$$
Dynamic Equation Solver
Equation: $$1x^2 – 5x + 6 = 0$$
Discriminant: $$D = 25$$
Roots: $$x_1 = 3, \quad x_2 = 2$$
Step-by-Step Factoring Method:
or $x^2 – 3x – 2x + 6 = 0$
or $x(x – 3) – 2(x – 3) = 0$
or $(x – 3)(x – 2) = 0$
∴ $x = 3$ or $x = 2$
Modify Coefficients ($y = ax^2 + bx + c$)
3D Paraboloid Modifiers ($z = a(x^2 + y^2)$)
Interact with a real-time 3D coordinate mesh mapping of quadratic values. Modify $a$ and see the mesh invert and bend dynamically.
Mesh Coordinate Metrics:
Render FPS: ~60 FPS
Vertices Count: 961 Points
Coordinate Grid Scale: -10 to +10
Class 10 Board-Style Practice Generator
Solve the given quadratic expression: $2x^2 – 11x + 15 = 0$.
Line-by-Line Solution Guide:
Nepal Board Standard Compulsory Practice Quiz
What is the nature of the roots for $x^2 – 6x + 9 = 0$?
Master of Algebra Game: Match the Roots!
Rules: Select an equation card on the left, then match it with the correct roots card on the right. Achieve correct pairs to earn stars, coins, and bonus chimes.
Equations Card Deck
Roots Match Card Deck
Bilateral AI Compulsory Math Guide
Class 10 Expert Assistant • Sridhar Acharya Formula Specialist
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