Latest Elitmus Aptitude Question SOLUTION: how many values of c in the equation x^2-5x+c=0 results in rational roots which are integers?

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(#M40153806) ELITMUS General Ability question quantitative Keep an EYE

how many values of c in the equation x^2-5x+c=0 results in rational roots which are integers?

Asked In Elitmus sukriti singh (8 years ago)

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Santosh Uplawdiya  (8 years ago)

The value of x can be calculated as:
x=( 5 +- sqrt(5^2 -4c))/2
For c = 0 , 4 , 6 , -6, -14, -24 , -36, -50 ……….and so on we can get rational roots which are
Integers.
Hence the Answer is :- Infinite

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Santosh Uplawdiya  (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 !!

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sukriti singh  (8 years ago)

will u plz explain????? santosh uplawdiya

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Ram Aasre Lodhi  (8 years ago)

Please explain in detail

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