Latest Elitmus Aptitude Question SOLUTION: 2) How many values of C in the equation x^2 – 5C + C result in rational roots which are integers?

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(#M40155978) ELITMUS Numerical Ability question Keep an EYE

2) How many values of C in the equation x^2 – 5C + C result in rational roots which are
integers?

Asked In Elitmus insha singh (8 years ago)

Unsolved Read Solution (6)

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Read Solution (6) :

akanksha jaiswal  (8 years ago)

something is missing in this question.the question should be x^2 - 5cx + c
the linear coefficient is the opposite of the sum of the roots and the constant term is their product. That is,

(x−r1) (x−r2) =x2 − (r1+r2)x + r1r2(x−r1)(x−r2) = x2 − (r1+r2)x + r1r2
so here r1=k and r2=5-k and c=r1r2
roots are
r1 r2 c
0 5 0
1 4 4
2 3 6
. . .
. . .
. . .
.

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insha singh  (8 years ago)

where has the 'c' gone from '5cx'? @akanksha

Is this solution Helpfull? Yes | No (2)  

swati das  (8 years ago)

Where is the answer? @AKANKSHA JAISWAL

Is this solution Helpfull? Yes | No (1)  

KIRAN KUMARI  (8 years ago)

x^2-5c+c=0
=> x=sqrt(5c-c)
now put the values of c by hit and trial method
so x=2 for c=1 and x=4 for c=4
the values of x are rational no intergers.

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praveen  (8 years ago)

ans is ---4

we have,by quadratic roots x= -b+-(b^2-4ac)/2a
so, if we check the possible values of c which outcomes the value of x as rational integers.
we will have


0,4,6,-6 are the possible values of c

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Digesh Singh Bisht  (1 year ago)

value of C will be infinite.

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