how many value of c in the equation x 2-5x c result in the rational root which are integer option

4)infinity.
10 years agoHelpfull: Yes(2) No(0)
For equation to have rational roots, Discriminant of the given equation should be positive and should have value equal to perfect square .
Now D= b^2 -4ac = 25 - 4c
So to have D positive and perfect square there could be infinite value of c.
So Ans is option 4.) infinite.
9 years agoHelpfull: Yes(2) No(0)
Option 4) infinite

But satisfy this
C
10 years agoHelpfull: Yes(1) No(0)
ans is opton 3. 1.....coz the value of c should be 6
10 years agoHelpfull: Yes(0) No(2)
answer is option 1(6) as for the rational root to be integer the discriminant should be a perfect square and that happens at 6 instances(0,1,4,9,16,25) as c
10 years agoHelpfull: Yes(0) No(2)
option 4 that is infinite solution
10 years agoHelpfull: Yes(0) No(0)
infinite as c can take negative values too.
10 years agoHelpfull: Yes(0) No(0)
ans is infinite bcz 5 can be written as
4+1,3+2,7-2,9-4..........................................
so any value of c can be infinite.
10 years agoHelpfull: Yes(0) No(0)
b^2-4ac must b a perfect square no..
5^2-4c must b a perfect square
c=6
only 1 value of c can satisfy above condition
ans=1
9 years agoHelpfull: Yes(0) No(0)
for rational roots b^2-4a*c
9 years agoHelpfull: Yes(0) No(0)
for root to be rational D>0 and is a perfect sqaure
d=25-4c
for c=0,c=4,c=6 the condition satisfied
9 years agoHelpfull: Yes(0) No(0)

how many value of c in the equation x^2-5x+c result in the rational root which are integer?

option 1.) 6
option 2.) 3
option 3.) 1
option 4.) infinite