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IPMAT Quadratic Equations Questions 2026
IPMAT Quadratic Equations questions are an important part of the IPMAT Quant section. These questions test how well you understand basic quadratic Equations concepts used in different problem types like solving quadratic equations, finding roots, checking the nature of roots, forming equations, and using factorization or formula methods.
You may get quadratic Equations questions as direct formula-based sums or as part of longer word problems. The good thing is, they become much easier once your basics are clear and you know which method to apply. You do not need very advanced math, just a strong understanding of concepts, regular practice, and careful calculation.
In this blog, you will find a simple formula PDF, a set of practice questions with answers, and some extra questions to solve on your own. You will also learn about common mistakes students make and a few easy tips to save time in the exam.
Important Formulas for IPMAT Quadratic Equations Questions
You only need a few basic formulas to solve most quadratic equations in IPMAT. These formulas help you find roots, identify the nature of roots, and solve equations quickly.
You can download the full formula PDF from the link above. Here is a quick look at some of the main ones:
Concept | Formula |
Standard Form of Quadratic Equation | ax² + bx + c = 0 |
Quadratic Formula | x = (-b ± √(b² - 4ac)) / 2a |
Discriminant | D = b² - 4ac |
If D > 0 | Roots are real and distinct |
If D = 0 | Roots are real and equal |
If D < 0 | Roots are imaginary / not real |
Sum of Roots | -b / a |
Product of Roots | c / a |
Forming equation from roots α, β | x² - (α + β)x + αβ = 0 |
These formulas are useful for solving questions on finding roots, checking the type of roots, forming quadratic equations, and solving application-based problems that often appear in IPMAT.
Top 5 Common Mistakes to Avoid in IPMAT Quadratic Equations Questions
Forgetting basic formulas: Make sure you remember the quadratic Equations formula, discriminant formula, and the relations between roots and coefficients.
Using wrong signs: Many students make mistakes while substituting values of a, b, and c, especially with negative signs.
Ignoring the discriminant: Always check the discriminant carefully when the question asks about the nature of roots.
Making factorisation mistakes: Sometimes, students factor the equation incorrectly and get incorrect roots.
Calculation errors: Even when the method is correct, small mistakes in square roots or simplification can give the wrong answer. Solve step by step.
List of IPMAT Quadratic Equations Questions
Here’s a short set of IPMAT-style quadratic Equations questions to help you practice. These include all common types of questions based on solving equations, finding roots, checking the nature of roots, and forming equations. Practice these regularly to become faster and more confident before your IPMAT exam.
Question 1
Let $$\alpha$$, $$\beta$$ be the roots of $$x^{2} - x + p = 0$$ and $$\gamma$$, $$\delta$$ be the roots of $$x^{2}- 4x + q = 0$$ where p and q are integers. If $$\alpha, \beta, \gamma, \delta$$ are in geometric progression then p + q is
correct answer:- 1
Question 2
Let $$f(x) = a^2x^2 + 2bx + c$$ where, $$a \neq 0, b, c$$ are real numbers and x is a real variable then
correct answer:- 2
Question 3
If the harmonic mean of the roots of the equation $$(5 + \sqrt{2})x^{2} − bx + 8 + 2\sqrt{5} = 0$$ is 4 then the value of b is
correct answer:- 4
Question 4
If the polynomial $$ax^2 + bx + 5$$ leaves a remainder 3 when divided by $$x - 1$$, and a remainder 2 when divided by $$x + 1$$, then $$2b - 4a$$ equals
correct answer:- 11
Question 5
Let $$a_{1} a_{2}, a_{3}$$ be three distinct real numbers in geometric progression. If the equations $$a_{1}x^{2} + 2a_{2} x + a_{3} = 0$$ and $$b_{1}x^{2} + 2b_{2}x + b_{3} = 0$$ has a common root,then which of the following is necessarily true?
correct answer:- 2
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Question 6
If $$8x^2 - 2kx + k = 0$$ is a quadratic equation in x, such that one of its roots is p times the other, and p, k are positive real numbers, then k equals
correct answer:- 3
Question 7
Consider the polynomials $$f(x) = ax^{2} + bx + c$$, where a > 0, b, c are real, and g(x) = -2x. If f(x) cuts the x-axis at (-2,0) and g(x) passes through (a, b), then the minimum value of f(x) + 9a + 1 is
correct answer:- 3
Question 8
The number of real solutions of the equation $$x^2 - 10 \mid x \mid - 56 = 0$$ is
correct answer:- 4
