Roots

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satyavegi: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Sat Aug 13, 2011 1:07 am

by satyavegi » Wed Jun 06, 2012 1:38 am

Q)How many roots does the equation 2^x=x-1 have ?

A)0
B)1
C)2
D)3
E)4
[spoiler]
OA -A[/spoiler]

Can Someone explain the concept here

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Source: Beat The GMAT — Problem Solving | Wed Jun 06, 2012 1:38 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Jun 06, 2012 3:02 am

satyavegi wrote:Q)How many roots does the equation 2^x=x-1 have?

Probably the easiest and least time consuming method to solve this problem is to apply the concept of graphs. The concept is : the number of solutions or roots of the equation f(x) = g(x) are the number of points at which the graphs of f(x) and g(x) intersects each other. (f(x) and g(x) are functions of x)

In this case, let us assume f(x) = 2^x and g(x) = (x - 1)
Now their graphs will be as shown in the following figure,

As they do not intersect at any point, there is no solution or roots of the equation 2^x = x - 1.

The correct answer is A.

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