IPMAT Quadratic Equations Formulas 2026 PDF, Download Now

IPMAT Quadratic Equations Formulas 2026

Quadratic equations is one of the most important topics in IPMAT Quant. It is a basic algebra chapter, but many questions in the exam are based on it. If your concepts are clear, you can solve these questions quickly and with better accuracy. This topic is also connected with other chapters like algebraic expressions, functions, graphs, and inequalities.

A quadratic equation is an equation of the form ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0, where a≠0a \neq 0a=0. In simple words, it is an equation in which the highest power of the variable is 2. Students should know the standard form, how to find the roots, and how to understand the nature of roots. If the basics are clear, this chapter becomes much easier to handle in the exam.

IPMAT Quadratic Equations Formulas PDF

An IPMAT Quadratic Equations Formulas PDF can help a lot during preparation. It gives all the important formulas and concepts in one place. This makes revision easy and saves time, especially before mocks and exams. Instead of reading long notes again and again, students can quickly revise from the PDF.

A good formula PDF should include the standard form of a quadratic equation, quadratic formula, nature of roots, sum and product of roots, factorisation method, and common question types. It should also have small examples so that students can understand how to apply the formulas in real questions. This is very helpful for quick learning and revision.

Students should use the PDF regularly, not only before the exam. If you revise these formulas again and again, they become easy to remember. This also helps in reducing silly mistakes in the exam.

List of all IPMAT Formulas PDFs

While preparing for IPMAT, students should not focus on only one topic. Quant has many important chapters, and each chapter has its own formulas. That is why it is useful to keep all IPMAT formula PDFs together for revision.

IPMAT Quadratic Equations Important Topics

Some parts of quadratic equations are asked more often in the IPMAT exam. So, students should know the important areas and prepare them well. The main topics include the standard form of a quadratic equation, solving by factorisation, solving by quadratic formula, nature of roots, discriminant, sum and product of roots, formation of quadratic equations, and word-based questions.

These subtopics are important because they are commonly used in exam questions. For example, some questions ask you to find the roots directly, while others ask you to check whether the roots are real, equal, or imaginary. In some questions, you may need to form the equation when the roots are given. So, it is important to understand the logic behind the topic, not just the formula.

Tips for Using the Quadratic Equations Formula PDF Effectively

To use the formula PDF properly, first read it after finishing the chapter. Then solve some practice questions based on it. This will help you understand how the formulas are used. Revise the PDF again before mocks and after mocks if you made mistakes in this topic.

You should also mark the formulas that you forget often. These are your weak areas and need more revision. Try to revise for a few minutes every day instead of studying it only once in a long session. Small daily revision helps a lot.

IPMAT Quadratic Equations Important Questions

IPMAT quadratic equations important questions help you understand how this topic is asked in the exam. These questions cover concepts like roots of equations, factorization, discriminant, and the nature of roots. Practicing them regularly can improve your speed, accuracy, and confidence in the Quant section.

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

A

-34

B

30

C

26

D

-38

Show Answer Explanation Video Solution

correct answer:- 1

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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

A

f(x) has a maximum and a minimum

B

f(x) has a minimum and no maximum

C

f(x) has a maximum and no minimum

D

f(x) has no minimum and no maximum

Show Answer Explanation Video Solution

correct answer:- 2

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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

A

$$4 - \sqrt{5}$$

B

2

C

3

D

$$4 + \sqrt{5}$$

Show Answer Explanation Video Solution

correct answer:- 4

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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

Show Answer Explanation Video Solution

correct answer:- 11

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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?

A

$$b_{1}, b_{2}, b_{3}$$ are in arithmetic progression

B

$$\dfrac{b_{1}}{a_{1}}, \dfrac{b_{2}}{a_{2}}, \dfrac{b_{3}}{a_{3}}$$ are in arithmetic progression

C

$$b_{1}, b_{2}, b_{3}$$ are in geometric progression

D

$$\dfrac{b_{1}}{a_{1}}, \dfrac{b_{2}}{a_{2}}, \dfrac{b_{3}}{a_{3}}$$ are in geometric progression

Show Answer Explanation Video Solution

correct answer:- 2