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(#M40008871) ELITMUS Numerical Ability question Keep an EYE

how many values of c in the equation x^2-5x+c result in rational roots which are intergers

Asked In Elitmus amrit bhagat (13 years ago)

Unsolved Read Solution (7)

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Read Solution (7) :

Ashu  (13 years ago)

There are many values of C which will result in rational roots which are integers ( positive and negative).

like c=6,-6,-14,-24,-50

Is this solution Helpfull? Yes (36) | No (11)  

ramesh kummara  (13 years ago)

Infinite..
c=4 => x=1,4
c=-6 => x=-1,6
c=-14 => x=-2,7
c=-24 => x=-3,8
c=-36 => x=9,-4
c=-50 => x=-5,10
c=-55 => x=-6,11 and so on...

Is this solution Helpfull? Yes (36) | No (8)  

Gagan Simlote  (10 years ago)

For roots of the equation X^2-5X+C to be rational integers we need to calculate its DISCRIMINANT (Dis) which should be greater than or equal to 0.
i.e.

Dis=b^2-4ac
Dis>=0

here b=-5 , a=1 , c=C

hence Dis=(-5)^2 -4*1*C = 25-4C
therefore we can write the inequality as

25-4C>=0

or
25>=4C

there are infinite values of C ranging from -infinity to +6

so wee have the infinite solutions for which the roots are rational integers

hence, the answer is infinite

Is this solution Helpfull? Yes (19) | No (1)  

sanjog kumar  (12 years ago)

x^2-5x+c
x=5+
























c=0,x=5or0
c=4,x=4or1
c=6,x=3or2
c=-6,x=6or-1
c=-14,x=7or-2
c=-24,x=8or-3
this will satisfy for infinite value of c.
hence,
answer=infinite

Is this solution Helpfull? Yes (8) | No (1)  

PANKAJ KUMAR TRIPATHI  (12 years ago)

infinite.
x=(5+(25-4c)^(1/2))/2
x=(5-(25-4c)^(1/2))/2
c=4,6,-6,-14,-24.....infinite

Is this solution Helpfull? Yes (6) | No (2)  

shreeprakash  (8 years ago)

since leading coefficient is one and coefficient of x is integer i.e -5 so for every integral value of 'c' for which equation has rational roots. then these rational roots must be integral.
and c is of the form given by

25 - 4c = (2*n +_ 1)^2

c =( 25 - (2*n +_ 1)^2)/4

n belongs to integer

so there exists infinitely many c.

Is this solution Helpfull? Yes | No (1)  

Digesh Singh Bisht  (2 years ago)

its infinite

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