Latest Elitmus Aptitude Question SOLUTION: how many values of c in the equation x^2-5x+c=0, results in rational roots which are integer. a) 1 b) 3 c) 0 d) infinite

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(#M40032814) ELITMUS Numerical Ability question inequality Keep an EYE

how many values of c in the equation
x^2-5x+c=0, results in rational roots which are integer.
a) 1
b) 3
c) 0
d) infinite

Asked In Elitmus Pawan Pandey (10 years ago)

Solved RAKESH Read Solution (7)

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RAKESH  (10 years ago)

x^2-5x+c=0
=> x= [5+-sqrt(25-4c)]/2

for, c = 0,4,6,-6,-14,-24,... we get rational roots which are integers
so,c has infinite no. of values.
d) infinite

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rahul jain  (10 years ago)

roots will be x=(5+-sqrt(25-c))/2
now,for it to be an integer sqrt value must be odd as there is a 2 in divide.so we will look for those values of c which makes it a odd.values of c are 0,4,6..also we can have negative values...so options a,b,c are invalid.infinite is the answer

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vinod  (10 years ago)

it has infinite solutions some of the value of c are 6,4,-6,-14 etc...

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kumar sajan  (10 years ago)

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...
Hence, Infinite is the answer

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rohit kumar  (10 years ago)

ans-a
b^2-4ac>0
5^2-4*1*c>0
25-4c>=0
for c=4
9>0
so ans is 1 value of c is 4

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Lokesh Agrawal  (10 years ago)

comparing with x^2 - Sx + P=0;
S=5;
hence infinite pair of integers with sum=5;

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Ambe Pratap Singh  (9 years ago)

x^2-5x+c=0
=> x= [10+-sqrt(100-16c)]/4

for, c = 0,4,6,-6,-14,-24,... we get rational roots which are integers
so,c has infinite no. of values.
d) infinite

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