GMAT-MBA-Prep.com provides a free introductory course for the GMAT. This guide is designed to get your math and verbal skills up to speed so that you can make the most from a classroom or online GMAT course.
 
5b2. Quadratic Equations and Inequalities

Degree of an equation: The highest power of the variable is called the degree of the equation.


For example,


1. x + 2 = 3 Þ equation of degree one.


2. x2 + 2x + 3 = 0 Þ equation of degree two.


3. x3 + x2 + 4x - 2 = 0 Þ equation of degree three.


4. xn + 2xn-2 + .... = 0 Þ equation of degree n.


An equation of degree two is called a Quadratic Equation.


A quadratic polynomial is any polynomial equivalent to one of the form ax2 + bx + c.


A quadratic equation is any equation equivalent to one of the form ax2 + bx + c = 0.


Roots of an equation: Roots are those values of the variable parameter, which satisfies the equation. Degree of an equation gives the number of maximum roots possible for that equation.


By using formula:


If there is a quadratic equation of the form, then the roots of the equation is given by,



Inequalities


As in equalities we get the exact value of the variables in inequalities we don't. In inequalities we can only get a range of values for the variable, which can satisfy the in equation. In inequalities we do a relation comparison between the variables.


For example, if a > b and b > c then a > c. Here we don't know the values of a, b and c but we can compare which one is greater than the other.


Examples

(A) 4 < x < 16
(B) –4 > x > –16
(C) 4 > x > –16
(D) x < 16
(E) –16 < x < 4



Þ -6 < (10 - x) < 6


Þ-16 < -x < -4    Þ 4 < x < 16    Hence, (A)

 
GMAT(TM) and GMAT CAT (TM) are registered trademarks of the Graduate Management Admission Council(TM). The Graduate Management Admission Council(TM) does not endorse, nor is affiliated in any way with the owner or any content of this site.