Maximum number of real solution does the equation x^7+ax^5+bx^3+cx-d=0(a,b,c,d>0)

Dear Suraj

 

f’(x) = 7x^6 + 5ax^4 + 3b x^2 +c

 

this is always postive hence this is incresing function.

 

hence it will cut x axis only one time. hence number of real roots = 1

Dear student 

Here is the correct explanation 

f’(x) = 7x^6 + 5ax^4 + 3b x^2 +c
This is greater than zero 
Because a, b , c , d > 0 
f'(x) > 0
=> This indictes it is monotonically increasing 
Lim (x->-inf. ) f(x) = -infinity 
Lim (x->inf. ) f(x) =  infinity 
So, it has maximum real roots = 1 
Complex real roots = 7-1 =6