How Many Values Of C In The Equation X^3-5x+c Result In Rational Root

1.	How Many Values Of C In The Equation X^3-5x+c Result In Rational Roots Which Are Integers?
Answer» 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 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

How Many Values Of C In The Equation X^3-5x+c Result In Rational Roots Which Are Integers?

Answer»

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

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