Re: Which of the following represents the complete range of x over which
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07 Apr 2021, 04:30
x^3–4x^5<0
taking x^3 common
x^3(1-4x^2)<0
x^3(1-2x)(1+2x)<0
a.b.c<0 implies either one is negative and two is positive OR all are negative
Hence,
case 1) All are negative
x^3<0 and 1-2x<0 and 1+2x<0
x<0 and x>1/2 and x<-1/2
No solutions
case 2) one is negative rest positive
case a) x^3<0 and (1-2x)>0 and (1+2x)>0
-> x<0 and x<1/2 and x>-1/2
-> x belongs to (-1/2,0)
case b) x^3>0 and (1-2x)<0 and (1+2x)>0
-> x>0 and x>1/2 and x>-1/2
-> x belongs to (1/2,inf)
case c) x^3>0 and (1-2x)>0 and (1+2x)<0
-> x>0 and x<1/2 and x<-1/2
-> no solution
Hence, the final answer is
(-1/2,0) and (1/2,inf)
Hence correct answer is C