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द्विघात समीकरण (Quadratic Equations) Notes

Home / Class Notes / Class 10 / Math / द्विघात समीकरण (Quadratic Equations)
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About these notes

Class 10 Math द्विघात समीकरण (Quadratic Equations) notes give clear definitions, key formulas and concise revision for CBSE and Bihar Board students. Main sub-topics: standard form ax² + bx + c = 0, sum and product of roots, graph of a parabola, vertex and axis, forming equations from given roots, and common exam-style word problems. Use these notes for quick revision, then practise important questions and MCQ and try the chapter test and board-pattern mock tests on Merit Spring ROH to check readiness for school and board exams.

Key points you will learn

  • Class 10 Math द्विघात समीकरण (Quadratic Equations): standard form ax² + bx + c = 0 and degree 2
  • Sum and product of roots: if roots α and β then α + β = -b/a and αβ = c/a
  • Discriminant Δ = b² - 4ac; Δ>0 two real distinct roots, Δ=0 repeated root, Δ
  • Quadratic formula x = [-b ± √(b² - 4ac)]/(2a) and method of completing the square
  • Vertex and axis: axis x = -b/2a, vertex at ( -b/2a, -Δ/4a )
  • Factorisation method and using factors (गुणनखंड); forming equation from given roots
  • Exam tips: always check a ≠ 0, simplify before applying formula, substitute roots to verify

What is inside this chapter

Notes for this chapter will be added soon.

Questions students ask

What are the main methods to solve quadratic equations?

Factorisation, completing the square and the quadratic formula are the principal methods. Use factorisation when integer factors exist, completing the square to find the vertex, and the quadratic formula for any a, b, c (works even when roots are irrational).

How does the discriminant tell the nature of roots?

Compute Δ = b² - 4ac; if Δ>0 there are two distinct real roots, Δ=0 gives one repeated real root, and Δ

Where to find Class 10 Math द्विघात समीकरण notes and important questions?

Visit the Merit Spring ROH chapter page for CBSE and Bihar Board notes; you can use those notes for revision, then attempt the chapter test and board-pattern mock tests available site-wide to practise and assess preparation.

How to form a quadratic equation when roots are given?

If roots are α and β the monic quadratic is x² - (α + β)x + αβ = 0. For a leading coefficient a ≠ 1 use a[x² - (α + β)x + αβ] = 0 and expand to compare coefficients.

← Previous chapter दो चरों वाले रैखिक समीकरण युग्म (Pair of Linear Equations in Two Variables)

More Math chapters

Real Numbers Polynomials Pair of Linear Equations in Two Variables Quadratic Equations Arithmetic Progressions Triangles All chapters →

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