CAT Quadratic Equation topic from the quantitative aptitude section is considered one of the important topics. Around 1-2 direct questions can be expected from this section of moderate difficulty level. For preparation of CAT Quadratic Equation, candidates can invest at least 2 hours. From the section of CAT Quadratic Equation, multiple choice questions and numerical types of questions can be framed in CAT 2021 by the conducting body. Download CAT Previous Years Question Paper
While preparing for CAT Quadratic Equations topics, you need to focus on basics like the quadratic equations have only two roots and the nature of roots can be real or imaginary. Knowledge of these basic concepts will help you in solving the questions faster. Read the article to know more about the important formulas, basics concepts and solved sample samples. Also Check CAT QA Syllabus
What is the Quadratic Equation?
In algebra of Mathematics, a quadratic equation can be defined as any type of equation which is rearranged in a quality form and the form can be classified
- as ax^{2}+bx+c=0 where x denotes an unknown.
- On the other side, a, b, and c denotes known numbers, and a ≠ 0.
- If a is equal to 0, then that equation can be defined as linear, not quadratic because of the absence of ax^2 term.
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Approach to Solve CAT Quadratic Equation
CAT Quadratic Equations can be solved by using the following 3 methods:
- Factoring
- Quadratic formula
- Completing the square
| Using Factoring | Using Quadratic Formula |
|
 |
How to Check the Nature of Roots in CAT Quadratic Equations?
- If b2 – 4ac = 0
- then the equation will have equal roots.
- If b2 – 4ac < 0
- then the equation will have imaginary roots.
- If b2 – 4ac > 0
- then the equation will have real roots.
- If D is a perfect square
- then the equation will have rational roots.
- If D is not a perfect square
- then the equation will have irrational roots.
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| How to Prepare for CAT Mensuration? | How to Prepare for CAT Trigonometry? | Shortcut Methods for CAT QA |
CAT Quantitative Aptitude Quadratic Equation: Important Formulas
| Particular | Details | Formulas |
|---|---|---|
| Basic Formula | Roots of the Quadratic Equation | x = (-b ± √D)/2a where D = b2 – 4ac |
| Quadratic equation | In the form of roots | x2 – (α+β)x + (αβ) = 0 |
| Pairs | Roots are the conjugate pair of each other | (α + iβ), (α – iβ) |
| Addition | Sum of roots | S = α+β= -b/a = coefficient of x/coefficient of x2 |
| Multiplication | Product of roots | P = αβ = c/a = constant term/coefficient of x2 |
| Cubic Equation | If ax3 + bx2 + cx + d = 0 | Then α + β + γ = -b/a, αβ + βγ + λα = c/a, and αβγ = -d/a |
| Nature of Roots | Real and distinct | D > 0 |
| Real and equal | D = 0 | |
| Imaginary and unequal | D < 0 |
CAT Quadratic Equations Solved Questions
In the below section, some solved questions regarding CAT Quadratic Equations are given.
Ques. Find out the number of real solutions of the equation x2 - 7|x| - 18 = 0?
- 2
- 4
- 3
- 1
Correct Answer: ( 1 )
Ques. x2 - 9x + |k| = 0 has real roots. What are the number of integer values can 'k' take?
- 40
- 21
- 20
- 41
Correct Answer: ( 4 )
Ques. 2x + 5y = 103. What is the number of pairs of both the positive integers x and y that proved this equation.
- 9
- 10
- 12
- 20
Correct Answer: ( 2 )
Ques. Find out the number of real solutions for the equation x2 – 7|x| - 30 = 0
- 3
- 1
- 2
- none
Correct Answer: ( 3 )
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CAT Quadratic Equations Preparation Tips
In the below section, some important tips for CAT 2021 Quadratic Equations preparation are given below.
- Follow the book of class 6 or 7 to brush up the basic formulas and concept of Quadratic Equations
- Take a note of all the formulas and try to apply with the sample questions.
- Understand the nature of the graph where it is applicable.
- Try to solve all the problems step by step
- Give a mock test at least thrice in a week.
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