Quadratic Equation Questions for IPMAT 2027, Formulas and Preparation Tips

Overview: If you're preparing for IPM 2027, mastering Quadratic Equation Questions for IPMAT is essential for scoring well in the Quantitative Ability section. This is one of the most important Algebra topics, testing your conceptual understanding and problem-solving skills through both direct and application-based questions.

The key to solving IPMAT Quadratic Equation Questions is understanding the fundamentals: factorisation, the discriminant, completing the square, and the quadratic formula.

Once your concepts are clear, you'll be able to solve most questions quickly and accurately.

In this article, you'll find Quadratic Equation Questions for IPMAT 2027 along with detailed solutions and previous year-style practice problems to help you strengthen your concepts and improve your exam readiness.\

For better results, pair your preparation with IPMAT Last Year Question Papers, IPMAT Mock Tests, and other important Algebra topics like Linear Equations and Logarithms.

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Key Takeaways

• Build a strong understanding of the quadratic formula, discriminant, and nature of roots.

• Learn multiple methods of solving, such as factorisation and completing the square.

• Practice IPMAT PYPs and topic-wise problems regularly.

• Solve questions under timed conditions to improve speed and accuracy.

• Consistently revise your mistakes to strengthen concepts and boost confidence for IPMAT 2027.

What are Quadratic Equations Questions in 2027? 

Quadratic equations are a type of equation in algebra that can be rearranged in standard form as ax^{2}+bx+c=0, where x represents the unknown, a, b, and c represent known numbers, and a ≠ 0.

If a = 0, the equation is linear, not quadratic, as there is no ax^2 term.

Examples of the standard form of a quadratic equation (ax² + bx + c = 0) include:

• 6x² + 11x - 35 = 0
• x² -x - 3 = 0
• 2x² - 4x - 2 = 0
• -4x² - 7x +12 = 0
• 5x² - 2x - 9 = 0
• 20x² -15x - 10 = 0

Questions like these are common in the IPMAT entrance exam.

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Quadratic Equation Questions for IPMAT with Answers 2027

Here is the list of questions curated from the previous year's IPMAT question papers.

The subject mentor from Supergrads has solved the questions below with a detailed explanation. 

Solve these quadratic equations and enhance your preparation for the upcoming IPMAT exam.

Q1. If 𝛼 ≠ 𝛽 but α ² = 5α − 3 and β ² = 5β − 3 then the equation whose roots are 𝛼/𝛽 and 𝛽/𝛼 is

• (a) 3x ² − 25x +3 = 0
• (b) x ² + 5𝑥 −3 = 0
• (c) x ² − 5𝑥 +3 = 0
• (d) 3𝑥 ² − 19𝑥 + 3 = 0

Answer: D

Q2. Difference between the corresponding roots of x ² + ax+ b = 0 and x ² + bx + 𝑎 = 0 is same and 𝑎 ≠ 𝑏, then

• (a) 𝑎 + 𝑏 + 4 = 0
• (b) 𝑎 + 𝑏 − 4 = 0
• (c) 𝑎 − 𝑏 − 4 = 0
• (d) 𝑎 − 𝑏 + 4 = 0

Answer: A

Q3. If p and q are the roots of the equation x² + px + q = 0 then

• (a) 𝑝 = 1, 𝑞 = −2
• (b) 𝑝 = 0, 𝑞 = 1
• (c) 𝑝 = −2, 𝑞 = 0
• (d) 𝑝 = −2, 𝑞 = 1

Answer: A

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Q4. If a , b , c are distinct positive real numbers and a² + b ² + c ² = 1 then 𝑎𝑏 + 𝑏𝑐 + 𝑐𝑎 is

• (a) less than 1
• (b) equal to 1
• (c) greater than 1
• (d) any real no

Answer: A

Q5. The value of a for which one root of the quadratic equation (a² 2 − 5a+ 3)x ²2 + (3a − 1)x + 2 = 0 is twice as large as the other is

• (a) -2/3
• (b) 1/3
• (c) -1/3
• (d) 2/3

Answer: D

Read: How To Solve Algebra Questions for IPMAT 2027

Q6. If the sum of the roots of the quadratic equation ax² +bx + c = 0 is equal to the sum of the squares of their reciprocals, then a/c, b/a and c/b are in 

• (a) geometric progression
• (b) harmonic progression
• (c) arithmetic-geometric progression
• (d) arithmetic progression

Answer: B

Q7. Let two numbers have an arithmetic mean of nine and a geometric mean of 4. Then, these numbers are the roots of the quadratic equation

• (a) x ² + 18𝑥 −16 = 0
• (b) x ² − 18𝑥 +16 = 0
• (c) x ² + 18𝑥 +16 = 0
• (d) x ² − 18𝑥 −16 = 0

Answer: B

Q8. If (1 −𝑝) is a root of quadratic equation x² + 𝑝𝑥 +(1 −𝑝) = 0, then its roots are

• (a) 0, -1
• (b) -1, 1
• (c) 0, 1
• (d) -1, 2

Answer: D

Q9. If one root of the equation x²+ 𝑝𝑥 + 12 = 0 is four while the equation x ² + 𝑝𝑥 + 𝑞 = 0 has equal roots, then the value of q is

• (a) 3
• (b) 12
• (c) 49/4
• (d) 4

Answer: C

Q10.  If the roots of the equation x² −𝑏𝑥 + 𝑐 = 0 be two consecutive integers, then b ² −4𝑐 equals

• (a) 3
• (b) -2
• (c) 1
• (d) 2

Answer: C

Mastering quadratic equations is essential for cracking the IPMAT exam. Regular practice with various quadratic equation questions can significantly enhance your problem-solving skills and confidence. 

Furthermore, you take assistance from Supergrad's GMB study material.

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Quadratic Equation Questions for IPMAT 2027 with Explanations

Question 1

Solve the quadratic equation: x2−5x+6=0x^2 - 5x + 6 = 0x2−5x+6=0.

Question 2

Solve the quadratic equation: 2x2+3x−2=02x^2 + 3x - 2 = 02x2+3x−2=0.

Question 3

Find the roots of the quadratic equation: x2+4x+4=0x^2 + 4x + 4 = 0x2+4x+4=0.

Question 4

Solve the quadratic equation: x2−2x−8=0x^2 - 2x - 8 = 0x2−2x−8=0.

Question 5

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Solve the quadratic equation: 3x2+7x+2=03x^2 + 7x + 2 = 03x2+7x+2=0.

Additional Quadratic Equation Questions for IPMAT 2027

Question 1:

If x^2−5x+6=0, find the roots of the equation.

Question 2:

Find the value of k for which the equation x^2+kx+9=0 has equal roots.

Question 3:

Solve the quadratic equation 2x^2−7x+3=0 using the quadratic formula.

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Question 4:

The sum of two numbers is 10, and their product is 24. Find the numbers.

Question 5:

If one root of the quadratic equation x^2−3x+k=0 is 2, find k.

Question 6:

Find the nature of the roots of the equation x^2 - 4x + 5 =0.

Question 7:

If the roots of ax^2+bx+c=0 are reciprocal, show that c=ac = ac=a.

Question 8:

Find the sum and product of the roots of the quadratic equation 3x^2−7x+2=0.

Question 9:

Find the quadratic equation whose roots are 5 and −3.

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Question 10:

If one root of the equation x^2+px+12=0 is 3, find p.

Important Formulas to Solve Quadratic Equation Questions for IPMAT 2027

Here is the list of formulas that you can use to solve IPMAT practice Questions. 

• The standard form of a quadratic equation is ax² + bx + c = 0

• The discriminant of the quadratic equation is D = b² - 4ac

• For D > 0, the roots are real and distinct.

• For D = 0, the roots are real and equal.

• For D < 0, the roots do not exist, or the roots are imaginary.

• The formula to find the roots of the quadratic equation is x = 

• The sum of the roots of a quadratic equation is α + β = -b/a = - Coefficient of x/ Coefficient of x².

• The product of the Root of the quadratic equation is αβ = c/a = Constant term/ Coefficient of x²

• The quadratic equation having roots α, β, is x² - (α + β)x + αβ = 0.

• For positive values of a (a > 0), the quadratic expression f(x) = ax² + bx + c has a minimum value at x = -b/2a.

• For a negative value of a (a < 0), the quadratic expression f(x) = ax² + bx + c has a maximum value at x = -b/2a.

• For a > 0, the range of the quadratic equation ax² + bx + c = 0 is [b² - 4ac/4a, ∞)

• For a < 0, the range of the quadratic equation ax² + bx + c = 0 is : (∞, -(b² - 4ac)/4a]

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Preparation Strategy for IPMAT Quadratic Equation Questions 2027

1. Understanding the Importance of Quadratic Equation

Mastering questions on quadratic equations is essential to excel in the IPMAT exam. Though initially appearing complex, quadratic equation questions for IPMAT can be solved efficiently with the right approach.

This section will guide you through an effective preparation strategy, incorporating important concepts, formulas, and problem-solving techniques to help you ace the quadratic equation questions in the IPMAT exam.

2. Key Concepts and Formulas

Before diving into practice, ensure you understand the fundamental concepts and formulas related to quadratic equations:

1. Standard Form: A quadratic equation is generally written as ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0, where xxx is the variable, and a,b,a, b,a,b, and ccc are constants with a≠0a \neq 0a=0.

2. Discriminant: The discriminant (DDD) of the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0 is given by D=b2−4acD = b^2 - 4acD=b2−4ac. The discriminant determines the nature of the roots:

• D>0D > 0D>0: Two distinct real roots
• D=0D = 0D=0: Two equal real roots
• D<0D < 0D<0: No real roots (roots are complex)

3. Roots Formula: The roots of the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0 can be found using the quadratic formula:

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}x=2a−b±b2−4ac​​

4. Sum and Product of Roots:

• Sum of the roots (α+β\alpha + \betaα+β): −ba-\frac{b}{a}−ab​
• Product of the roots (αβ\alpha \betaαβ): ca\frac{c}{a}ac​

Problem-Solving Techniques

To solve quadratic equation questions effectively, use these methods:

Factorization:

• Rewrite the equation in the form ax^2+bx+c = 0.
• Find two numbers that multiply to ac and add up to b.
• Factorise and solve for x.

Completing the Square:

• Rewrite the equation in the form ax2+bx=−cax^2 + bx = -cax2+bx=−c.
• Add and subtract  on both sides.
• Solve for x after simplifying.

Using the Quadratic Formula:

• Directly apply the quadratic formula to find the roots.

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Practice Regularly

Consistent practice is crucial for mastering quadratic equations. Work on various types of questions, including those involving:

• Basic factorization
• Special cases with real, equal, and complex roots
• Application of the quadratic formula

Time Management is Important

Practice solving quadratic equations within a time limit to improve speed and accuracy. Allocate specific time for each problem and gradually reduce it as you become more proficient.

Mock Tests and Revision

Incorporate quadratic equation questions for the IPMAT exam into your mock tests to simulate exam conditions. Regularly revising key concepts and formulas will reinforce your understanding and boost your confidence.

Conclusion

Mastering quadratic equations is crucial for excelling in the IPMAT exam. You can significantly enhance your mathematical abilities by understanding fundamental concepts, practising various problem-solving techniques, and regularly revising key formulas.

Read: Quick Tricks to Solve Multiplication Division Questions in IPMAT 2027