IIT JEE , AIEEE Forum - Mathematics , Algebra

magiclko

the number of equations of the form x³ - px +2 =0 (p is an integer), having atleast one rational root is ....

a) 0

b) 2

c) 3

d) 4

shubham_sachdeva

what is the answer is it 3??

magiclko

how u got it?????

rahul_c

p = [ (x^3) +2]/x

for maximum value of p dp/dx = 0

3 (x^3) - (x^3) -2 =0

which gives x= 1

therefore maximum value of p= 3

f(x) = x^3 -px +2

for real roots p should be greater than 0

number of values of p 1,2,3

hence number of equations is 3

shubham_sachdeva

rahul is absolutely correct

krishna.gopal

Well i am not sure of exact answer to this problem but am still osting here to point out a mistake.

Rahul for

p = (x^3+2)/x

p has a local minima at x=1 and not at a maxima (derivative equall to zero does not implies a maxima)

I am not sure of answer to this question but i can think of several values of p for which raional root exist

p=-1,x=-1

p=3, x=2

p=5, x=-2

So answer is most probably c (Or may be d but and b are surely ruled out)

magiclko

yeah answer is 3