Eduvista · Class 10 Mathematics
Quadratic Equations
A focused lesson and practice set. This page covers the concepts listed below; it is not a claim of complete chapter or syllabus coverage.
Learn the essentials
Standard form
A quadratic equation in x has the form ax² + bx + c = 0, where a ≠ 0. Its roots are the x values that make the expression zero.
Three solving routes
Try factorisation first; completing the square and the quadratic formula work more generally. For ax² + bx + c = 0, x = (−b ± √(b² − 4ac)) / 2a.
Discriminant
D = b² − 4ac. D > 0 gives two distinct real roots, D = 0 one repeated real root, and D < 0 no real roots.
Worked example
Solve x² − 5x + 6 = 0.
- Find two numbers with product 6 and sum −5: −2 and −3.
- Factor: (x − 2)(x − 3) = 0.
- Set each factor to zero: x = 2 or x = 3. Substitute to check both.
Memory trick
For a monic quadratic, look for two numbers that add to b and multiply to c. If they are awkward, use the formula.
Common mistakes
- Forgetting ± in the quadratic formula.
- Dividing by a variable and losing the zero root.
- Mixing up the sign of b when calculating D.
Practice recall
Tap a card to reveal the answer. These are original Eduvista study cards.
Original practice quiz
Choose one answer per question. You can change it and see why it is right or wrong.
Quick revision sheet
- Write the equation in standard form first.
- D = b² − 4ac determines the nature of real roots.
- Check answers by substitution.
- For a word problem, reject roots that do not fit its context.
Original Eduvista explanations and practice aligned to the named NCERT topic. Check your current textbook and school syllabus for the full prescribed scope. NCERT textbooks ↗
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