Class 10 Maths — Chapter 4: QUADRATIC EQUATIONS
Chapter 4: QUADRATIC EQUATIONS is a chapter in Class 10 Maths (NCERT), part of the CBSE NCERT curriculum followed by over 25 million students across India. This chapter covers 6 topics including Definition and Standard Form of Quadratic Equations, Representing Word Problems as Quadratic Equations, Identifying Quadratic Equations. BrainWeave provides free AI-powered explanations — by voice or text, in Hindi or English — with no signup required.
What you'll learn
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▸Definition and Standard Form of Quadratic EquationsCore conceptstandard formax²+bx+c=0degree 2polynomiala ≠ 0
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▸Representing Word Problems as Quadratic EquationsCore conceptword problemsmathematical representationformulate equationreal-life situationsproblem solving
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▸Identifying Quadratic Equationsverifysimplifycheck equationdegree of equationalgebraic manipulation
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▸Concept of Roots and SolutionsCore conceptrootsolutionsatisfies the equationzeroes of a polynomialvalue of x
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▸Solving Quadratic Equations by FactorisationCore conceptfactorisationsplitting the middle termlinear factorsfind rootssolve for x
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▸Solving Equations with Repeated Rootsrepeated rootsequal rootsidentical factorsperfect square trinomialdiscriminant
Chapter Summary
Understanding that a quadratic equation is a polynomial equation of degree 2, and being able to express it in the standard form ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0.
The ability to translate real-life scenarios and verbal descriptions into mathematical quadratic equations. This involves identifying the unknown variable and setting up the relationship described in the problem.
Checking whether a given algebraic equation is quadratic by simplifying it into its simplest form and verifying if it fits the standard form ax² + bx + c = 0.
Understanding that a 'root' or a 'solution' of a quadratic equation is a value that, when substituted for the variable, makes the equation true. This connects to the concept of zeroes of a quadratic polynomial.
Finding the roots of a quadratic equation by factorising the quadratic polynomial, typically using the 'splitting the middle term' method, and then setting each linear factor to zero.
Recognizing and solving quadratic equations where the factorisation process results in two identical linear factors, leading to two equal (or repeated) real roots.
Practice Questions from this Chapter
Tap "Get Solution" on any question to ask our AI tutor.
- Explain quadratic formula simply. Get Solution →
- Find more real-world quadratic examples. Get Solution →
- Trace the history of algebra. Get Solution →
- What is the standard form of a quadratic equation? Get Solution →
- For the equation ax² + bx + c = 0 to be a quadratic equation, which condition must be met? Get Solution →
- What is a real number α called if it satisfies the equation ax² + bx + c = 0? Get Solution →
- What is the maximum number of roots a quadratic equation can have? Get Solution →
- What is the name of the expression b² – 4ac? Get Solution →
Did you know?
- 💡 The equals sign was first used in 1557 by Welsh mathematician Robert Recorde.
- 💡 Ancient Babylonians solved quadratic equations over 4,000 years ago.
- 💡 The path of a thrown ball follows a parabolic curve, described by a quadratic equation.
- 💡 The concept of zero as a number originated in India around the 5th century AD.
- 💡 Our modern number system, with place value, was developed in ancient India.
Frequently Asked Questions
How many topics are covered in this chapter?
This chapter covers 6 key topics: Definition and Standard Form of Quadratic Equations, Representing Word Problems as Quadratic Equations, Identifying Quadratic Equations, Concept of Roots and Solutions, Solving Quadratic Equations by Factorisation, and more. The BrainWeave AI tutor explains each one with examples.
Is Chapter 4: QUADRATIC EQUATIONS important for board exams?
Yes — Class 10 is a CBSE board exam year, and every NCERT chapter is part of the syllabus. Use BrainWeave's AI tutor to master this chapter, then practice with the auto-generated quizzes and mind maps.
Can I get NCERT solutions for this chapter in Hindi?
Yes. BrainWeave's AI tutor supports Hindi, English, and Hinglish for both voice and text chat. Just ask your question in your preferred language.
Is BrainWeave free for Class 10?
Yes. BrainWeave's free Spark plan gives generous daily messages — enough for regular homework. Premium features unlock when you bring your own free Google Gemini API key.
Can I use voice chat for this chapter?
Absolutely. Tap the mic, ask any question about Chapter 4: QUADRATIC EQUATIONS, and the AI tutor will explain it back in voice and text.
How is BrainWeave better than static NCERT solutions sites?
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