Latest Elitmus Aptitude Question SOLUTION: Q. How many values of c in the Equation x^3-5x+c result in rational roots which are integers? Option a)1 b)3 c)0 d)infinite

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(#M40031892) ELITMUS Numerical Ability question Quadratic Equations Keep an EYE

Q. How many values of c in the Equation x^3-5x+c result in rational roots which are integers?
Option
a)1
b)3
c)0
d)infinite

Asked In Elitmus (10 years ago)

Unsolved Read Solution (6)

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RAKESH  (10 years ago)

x^3-5x+c=0
if x=1, 1-5+c=0 or c=4
if x=-1, -1+5+c=0 or c=-4
if x=2, 8-10+c=0 or c=2
if x=-2, -8+10+c=0 or c=-2
we see that,for c=-2,2,-4,4 we get x=-2,2,-1,1 etc
i.e we get integral roots of x for infinite values of c.

d)infinite

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kuldeep kushwaha  (10 years ago)

d)infinite

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rohitashwa  (10 years ago)

roots to be rational root d=(b^2-4*a*c)=!a perfect square value so for c=1 ,d=21
c=2,d=25-4*2=17,c=5 d=25-20=5. thus answer 3.however see to be rational we 9 roots(x=b^2-4*a*c) and also to be rational it should be in form -b+-root(b^2-4*a*c)/4a.so d!=a perfect square.and also if no. of rational roots asked den it would be 6 as rational roots occur in conjugate pair.as you 9 roots =-b+-root(b^2-4*a*c)/4a.notice the sign after b it(roots) has one + and a -. i.e -b+-(m taking abt this signs)root(b^2-4*a*c).so no. of rational roots=6.however here it has only asked value of c where rational roots occur so answer 3(1,2,5). hope every body would like it. if disagree bhad mai jao.!!!!!!!!!!!!:)

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Neeraj kumar jha  (10 years ago)

Rakesh is right...Rohit what u r saying is for equation like ax2+bx+c but here the equation is cubic.

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sfsdf  (10 years ago)

see unless u know the value of c u cannot jump to the conclusion of finding a rational root so depending upon the constant we can find the roots so its infinite

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Karishma sahu  (10 years ago)

can u please explain??

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