if x + 1/x = 4 then how many integers are there between the roots of this equation.

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07 Feb 2013 equation

if x + 1/x = 4
then how many integers are there between the roots of this equation.

OPtion

1) 0
2) 1
3) 2
4) 3
5) 4
6) 5
7) 6
8) 7
9) no real roots so nothing can be said
10) none of these

Solution

on solving roots are .268 and 3.732
so answer = 3
second method
on putting x=0 value of expression = 1
x=1 = -2
x=3 = -2
x=4 = 1
so 1, 2 and 3 are possible answers

Correct Option: 4 Best Solution (10)

vigneshwari   11 years AGO

we can simplify the given eqn as
x^2 - 4x + 1 = 0
then x = [-(-4)+sqrt(16-4)]/2 or
x = [-(-4)-sqrt(16-4)]/2
=> x = 4+2sqrt(3) / 2 or 4-2sqrt(3) /2
=> x = 2+sqrt(3) or 2-sqrt(3)
=> x = 2+1.732 or 2 - 1.732
=> x = 3.732, 0.268
Therefore, 1,2,3 are the only integers between the above two roots.
Hence the required number of integers 3.

Like? Yes (5) | No (1)  

Rats   11 years AGO

The roots are 2+1.414(3.414) and 2-1.414(0.586)
So there are 3 integers between roots i.e(1,2,3).

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MANOJ TIWARI   11 years AGO

all roots are irrational, not a single root is an integer. x+1/x=4 => x^2-4x+1=0,x=2+sqrt(3) ans 2-sqrt(3). so ther are 4 integers b/n the roots 0,1,2,3

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Devendra Marghade   11 years AGO

x + 1/x = 4
x^2-4x+1=0
Roots of the equation are 2-rt(3),2+rt(3)
2-1.732=0.268 & 2+1.732=3.732
So the integers between the roots are 1,2,3

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abhishek mishra   11 years AGO

by disc method roots are0.27 and 3.73 so integers will be 1,2 and 3

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jitendra singh   11 years AGO

roots are 2+1.73&2-1.73
so 1,2,3 are three integer between roots

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Vinay Sipani    11 years AGO

x^2 + 1 = 4x
x^2 - 4x + 1 = 0

roots are (2 + sqrt3) and (2 - sqrt3)
=>integers b/w these = 1,2 and 3
=> 3 integers.

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sc mandota   11 years AGO

values are .268 and 3.732
so integers are 1,2,3

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PRATHAM MEHROTRA   11 years AGO

roots are 2+root(3),
2-root(3)

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Sneha Agarwal   11 years AGO

the roots are 2+-sqrt(3)
integers are 1,2,3.

Like? Yes (1) | No