Elitmus
Exam
Numerical Ability
Quadratic Equations
how many values of c in the equation x^2-5x+c result in rational roots which are intergers
Read Solution (Total 7)
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- There are many values of C which will result in rational roots which are integers ( positive and negative).
like c=6,-6,-14,-24,-50 - 12 years agoHelpfull: Yes(36) No(11)
- Infinite..
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... - 12 years agoHelpfull: Yes(36) No(8)
- For roots of the equation X^2-5X+C to be rational integers we need to calculate its DISCRIMINANT (Dis) which should be greater than or equal to 0.
i.e.
Dis=b^2-4ac
Dis>=0
here b=-5 , a=1 , c=C
hence Dis=(-5)^2 -4*1*C = 25-4C
therefore we can write the inequality as
25-4C>=0
or
25>=4C
there are infinite values of C ranging from -infinity to +6
so wee have the infinite solutions for which the roots are rational integers
hence, the answer is infinite - 10 years agoHelpfull: Yes(19) No(1)
- x^2-5x+c
x=5+
c=0,x=5or0
c=4,x=4or1
c=6,x=3or2
c=-6,x=6or-1
c=-14,x=7or-2
c=-24,x=8or-3
this will satisfy for infinite value of c.
hence,
answer=infinite
- 12 years agoHelpfull: Yes(8) No(1)
- infinite.
x=(5+(25-4c)^(1/2))/2
x=(5-(25-4c)^(1/2))/2
c=4,6,-6,-14,-24.....infinite - 12 years agoHelpfull: Yes(6) No(2)
- 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. - 8 years agoHelpfull: Yes(0) No(1)
- its infinite
- 2 years agoHelpfull: Yes(0) No(0)
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