Latest Elitmus Aptitude Question SOLUTION: how many values of c in equation x^2-5x+c result rational roots which are integers. (a) 1 (b) 3 (c) 6 (d) infinite

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(#M40152125) ELITMUS Numerical Ability question quadratic Keep an EYE

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

(a) 1 (b) 3 (c) 6 (d) infinite

Asked In Elitmus prem kishor (8 years ago)

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Abhishek nkumar  (8 years ago)

w.k.t D=b^2- 4 a c >0 for rational roots
= (-5)^2-4*1*c > 0
hence values of c can be either positive or negative
c=0,1,,2,3,4,5,-1,-2,-3,-4,-5...
there is no unique values for c hence ans. will be infinte..option d is correct

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SURAJIT SAHA  (8 years ago)

its mentioned that the roots have to integers, which implies both positive as well as negative integers. Also there is no such constraint on c if it has to be positive or negative.
Such a condition can be satisfies by infinite values of c.
For eg. X^2-5X-36, which have roots 9, -4
X^2-5X-14, which have roots 7, -2

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Saumya  (8 years ago)

for rational roots...
b^2-4ac>0
=>25-4*1*c>0
=>25>4c
=>cc can be6 ,5, 4,3,2,1,0........
(since they all are integers)
so, ans is infinite.

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Mike Ross  (8 years ago)

the value of c can either be 4, 6 or 0 so ans is 3

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MANIAKANDAN  (8 years ago)

ans:6 sol: -3*-2=6

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Jagriti Goswami  (8 years ago)

Ans: d)infinite
See this link for explanation: https://www.quora.com/How-many-values-of-C-in-the-equation-x-2-5x+c-result-in-rational-roots-which-are-integers

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