Last Updated: 11 May 2026
IPMAT 2027 Quantitative Aptitude carries 3-4 questions on Quadratics across IIM Indore + IIM Rohtak forms. With IIM Indore IPM cutoff at 79.5/100 in 2026, missing even one of these is costly.
Standard Form
ax² + bx + c = 0 where a ≠ 0.
Quadratic Formula
x = [-b ± √(b² – 4ac)] / 2a; D = b² – 4ac is the discriminant.
Nature of Roots (using D)
| D Value | Nature of Roots |
|---|---|
| D > 0 and perfect square | Real, distinct, rational |
| D > 0 and not perfect square | Real, distinct, irrational |
| D = 0 | Real, equal |
| D < 0 | Imaginary (complex conjugates) |
Vieta’s Formulas
If α, β are roots of ax² + bx + c = 0:
- Sum of roots: α + β = -b/a
- Product of roots: αβ = c/a
- α² + β² = (α+β)² – 2αβ
- α³ + β³ = (α+β)³ – 3αβ(α+β)
- (α-β)² = (α+β)² – 4αβ = D/a²
- 1/α + 1/β = -b/c
Symmetric Functions of Roots
If S₁ = α+β and S₂ = αβ, then any symmetric function can be expressed in S₁ and S₂.
- α² + β² = S₁² – 2S₂
- α³ + β³ = S₁(S₁² – 3S₂)
- α⁴ + β⁴ = (S₁² – 2S₂)² – 2S₂²
Forming a Quadratic from Roots
If sum = S and product = P, equation: x² – Sx + P = 0.
Quadratic Inequalities
- Solve ax² + bx + c > 0 by finding roots and using sign-chart.
- If a > 0: positive outside roots, negative between.
- If a < 0: negative outside, positive between.
- If D < 0 and a > 0: always positive.
Common Roots of Two Quadratics
If a₁x² + b₁x + c₁ = 0 and a₂x² + b₂x + c₂ = 0 have one common root:
(c₁a₂ – c₂a₁)² = (a₁b₂ – a₂b₁)(b₁c₂ – b₂c₁)
Maximum / Minimum of Quadratic
For f(x) = ax² + bx + c:
- If a > 0: minimum at x = -b/(2a); min value = c – b²/(4a) = -D/(4a).
- If a < 0: maximum at the same x.
IPMAT-Specific Twists
- Often combined with logarithm: log(quadratic) inequalities.
- Roots in terms of trigonometric identities (occasional IIM Indore).
- Integer-root finding using rational root theorem.
- Maximum value of compound functions like (x² + 6x + 10)/(x² + 6x + 8).
Internal Links
FAQ
How many marks from Quadratic in IPMAT?
12-16 marks (3-4 questions across QA-MCQ and QA-SA).
Are short-answer questions on this topic?
Yes — IIM Indore consistently puts 1-2 QA-SA (Quant Short Answer) on quadratic roots/coefficients.
Best book for IPMAT Quadratic?
Arun Sharma ‘How to Prepare for QA’; Sarvesh Verma for shortcut formulas.
Practice Quiz
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