Question

find solution of the following by wavy curve method :-
(x-2)⁷ (x+5)⁶ (x²+x+2)
————————————— ≤ 0
(x-3)⁴​

Answer 1

Answer:

(x3+1)(x2–1)2(x+2)3≥0

(x+2)3(x+1)3(x−1)2(x2−x+1)≥0

The expression has 3 zeroes at x=−2

3 zeroes at x=−1 and 2 zeroes at x=1 ; The expressionx2−x+1does not yield any zero.

Count of zeroes to the right.

x>1 0 zeroes. Expression is positive.

-1<x<1 2 zeroes. Expression is positive.

-2<x<-1 5 zeroes. Expression is negative .

x<-2 8 zeroes. Expression is positive.

Even number of zeroes to the right makes the expression positive.

(−∞,−2]∪[−1,∞)is the range of x.