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Quadratic Equations — Revision Notes

Gujarat Board · Class 10 · Mathematics

Quadratic Equations revision notes for Gujarat Board Class 10 Mathematics: 4 topics in quick points. Includes What is a Quadratic Equation?, Solving by.

45 questions30 flashcards8 formulas & key relations5 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 What is a Quadratic Equation?, Solving by Factorisation, Solving by Completing the Square, The Quadratic Formula. Study these first, then practise questions on each for the Gujarat Board Class 10 board exam.
How should I revise Quadratic Equations for the Gujarat Board Class 10 board exam?
Learn the core ideas first, then work through the 45 practice questions on Quadratic Equations. Revise 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.

More resources for Quadratic Equations

All Gujarat Board Class 10 Mathematics Revision Notes

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