JEE Quadratic Equations Quiz
Practice on the discriminant and nature of roots, relations between roots and coefficients, common roots, and the location of roots relative to a given number.
Skill map
Levels in this jee quadratic equations quiz
Every question is generated fresh by AI and calibrated to your level - clear a level and the next one gets harder. Miss one and the AI tutor explains Quadratic Equations until it sticks, then aims a follow-up at the gap. Want to grind one level? Start the quiz and type that sub-topic as your own.
Exam focus
How Quadratic Equations is asked
A consistently present chapter that also feeds Complex Numbers, Functions and Calculus. Questions increasingly ask about the location of roots relative to a number rather than about solving directly, which is a graph-based skill rather than a formula-based one.
Cheat sheet
Quadratic Equations formulas worth memorising
| Quantity | Formula |
|---|---|
| Roots | x = (−b ± √(b² − 4ac)) / 2a |
| Discriminant | D = b² − 4ac |
| Sum of roots | α + β = −b/a |
| Product of roots | αβ = c/a |
| Difference of roots | |α − β| = √D / |a| |
| Equation from roots | x² − (α + β)x + αβ = 0 |
| Vertex of the parabola | x = −b/2a |
Marks lost here
Common mistakes in Quadratic Equations
- Forgetting to check a ≠ 0. If the coefficient of x² contains a parameter, the equation may be linear for some values, and questions frequently make that the whole point.
- Assuming D > 0 guarantees real distinct roots without checking that the coefficients are real. For complex coefficients the discriminant test does not apply as stated.
- Solving inequalities by cross-multiplying. Multiplying by an expression whose sign is unknown can flip the inequality - use a sign chart on the factorised form instead.
- Treating 'both roots positive' as only requiring a positive product. You need D ≥ 0, a positive sum and a positive product together; any one alone is insufficient.
- Ignoring the sign of a when reasoning about maxima and minima. The parabola opens upward for a > 0 and downward for a < 0, which reverses which vertex value is the extremum.
Game rules
How a round works
- 01Spawn
Press play - the AI generates Quadratic Equations questions in seconds.
- 02Level up
Answer to earn XP and build a streak. Difficulty adapts to your accuracy and speed.
- 03Learn or lose
Every answer - right or wrong - gets an AI tutor explanation. Wrong answers respawn as follow-ups.
Leaderboard
Quadratic Equations high scores
Next challenges
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Player's guide
JEE Quadratic Equations Quiz - FAQs
How do I handle 'location of roots' questions?
Draw the parabola rather than solving. Three conditions cover almost every case: the sign of the discriminant, the sign of f(k) at the point of interest, and the position of the vertex −b/2a relative to k. Sketching turns an algebra problem into a picture.
What is the condition for two quadratics to have a common root?
Subtract one equation from the other to eliminate the quadratic term, which gives the common root directly when it exists. If both roots are common, the coefficients are proportional: a₁/a₂ = b₁/b₂ = c₁/c₂.
Is the jee quadratic equations quiz free?
Yes - completely free, with no sign-up required. Type a topic, press start, and the AI generates an adaptive Quadratic Equations quiz with an explanation for every answer.
Can teachers host this jee quadratic equations quiz live for a class?
Yes - create a free teacher account, host a live room on "Quadratic Equations", and students join with a 6-character code at quff.in/join. No student accounts needed.
From the blog
Quadratic Equations guides & reading
JEE Quadratic Equations: 30 Practice Questions Solved
Thirty solved questions on quadratics, including the location-of-roots problems that are answered by sketching rather than solving.
Exam PrepJEE Limits: 30 Practice Questions with Full Solutions
Thirty solved Limits questions, starting from the check that decides the method: is the form actually indeterminate?
Exam PrepJEE Differentiation: 30 Practice Questions with Solutions
Thirty solved Differentiation questions, weighted toward applications of derivatives - which is where the paper actually puts its marks.
More exam prep quizzes
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Six adaptive Quadratic Equations questions. About two minutes. Climb the podium.