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Quadratic Equations

Gujarat Board · Class 10 · Mathematics

Quick revision notes for Quadratic Equations — Gujarat Board Class 10 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

45 questions30 flashcards5 concepts

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Key Topics to Revise

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1. What is a Quadratic Equation?

  • A quadratic equation in variable x is of the form ax² + bx + c = 0, where a, b, c are real numbers and a ≠ 0.
  • The word 'quadratic' comes from the Latin word 'quadratus' meaning square.
  • The highest power of the variable must be 2 for it to be quadratic.
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2. Solving by Factorisation

  • Factorisation means expressing ax² + bx + c as a product of two linear factors.
  • The method is based on the Zero Product Property: if P × Q = 0, then P = 0 OR Q = 0.
  • To split the middle term: find two numbers p and q such that p + q = b and p × q = a × c.
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3. Solving by Completing the Square

  • This method converts ax² + bx + c = 0 into the form (x + k)² = d, which is easy to solve.
  • First, make the coefficient of x² equal to 1 by dividing throughout by a.
  • Then, add and subtract (b/2a)² to complete the perfect square.
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4. The Quadratic Formula

  • The quadratic formula gives roots of ax² + bx + c = 0 directly using the values of a, b, and c.
  • Formula: x = (-b ± √(b² - 4ac)) / 2a
  • This formula is applicable for ALL quadratic equations — it never fails.

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Full Notes

Key Concepts

A quadratic equation in variable xA real number α is calledIf a quadratic equation ax² +This method transforms the quadratic equationFor any quadratic equation ax² +

Frequently Asked Questions

What are the important topics in Quadratic Equations for Gujarat Board Class 10 Mathematics?
Key topics in Quadratic Equations include Quadratic Equations: Complete Concept Map, Quadratic Equations – Complete Chapter Overview, Flowchart showing how the prayer hall problem leads to a quadratic equation. These are the concepts Gujarat Board Class 10 examiners draw on most — study them first, then practise related questions.
How to score full marks in Quadratic Equations — Gujarat Board Class 10 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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