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Math Book 1 : Quadratic Equations : Algebra

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Quadratic Equations in Algebra is a topic from which you could expect 2 to 3 questions in the GMAT quant section. The topic is an important one. Many questions that appear in this topic are word problems that expect you to write an equation from the information given and then solve it. The gist of what is tested is your ability to write the equation appropriately.

Quadratic Equations
2
Book 1

Concepts Covered

Quadratic Equations or equations of the second order where the variables have a power of 2 is tested. Solutions, roots, types of roots of quadratic equations are tested. Factorizing a quadratic equation to find its solutions is also tested in GMAT. 4GMAT's GMAT Math Lesson Book in this chapter covers the following concepts:

  1. Introduction to quadratic equations and roots of quadratic equations.
  2. Concept of discriminant of quadratic equation.
  3. Method to calculate the sum, difference and product of roots along with illustrative example.
  4. Method to form a quadratic equation, given its roots; explained with illustrative examples.
  5. Definition of conjugate roots.
  6. Concepts in quadratic equations such as common roots, minimum and maximum value of quadratic equations.
  7. Method to determine nature of roots (real, rational, equal, imaginary), using value of the discriminant.
  8. Method to determine the value and sign of roots using value and sign of the coefficients of the quadratic equation.
  9. What does a quadratic equation equation represent when plotted on an x-y plane?
  10. Types of curves for different values of the discriminant; when b2 - 4ac > 0; when b2 - 4ac = 0; when b2 - 4ac < 0
  11. 16 solved examples to explain above mentioned concepts.
  12. 18 exercise problems with the answer key and also explanatory answers.
  13. A multiple choice test with 34 questions from linear and quadratic equations along with explanatory answers and answer key as part of the work book.
Here is an example of a typical solved example in this chapter.

 

Sample Question

Question
If one root of the quadratic equation 14x2 + 5x - 1 = 0 is 2, what is the other root?

Explanatory Answer
Let a and b be the two roots of the quadratic equation given above.

The sum of the roots a + b = -b/a = -5/14

As one of the roots a is 2, and the sum of the roots is -5/14, the other root b = -5/14 - 2 = -33/14

Chapterwise details of 4GMAT's Math Lesson Books

Math Lesson Book 1
  1. Linear Equations
  2. Quadratic Equations
  3. Set Theory
  4. Sequences & Series
    Details | Quiz
  5. Number Theory
  6. Inequalities
    Details | Quiz
  7. Functions
Math Lesson Book 2
  1. Descriptive Statistics
  2. Ratio Proportion
    Details
  3. Mixtures
  4. Interest
    Details
  5. Rates : Speed Distance
  6. Rates : Races
    Details
  7. Rates : Pipes Cisterns
  8. Rates : Work Time
    Details
Math Lesson Book 3
  1. Percents
  2. Profits
    Details
  3. Permutation
  4. Probability
    Details
  5. Geometry
  6. Solid Geometry
    Details
  7. Coordinate Geometry