3. Quadratic Equations

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. 15 solved examples to explain above mentioned concepts
10. 18 exercise problems with the answer key and also explanatory answers
11. An objective type speed test with around 40 questions along with explanatory answers and answer key are provided for the speed test

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