If we solve the corresponding equation (x-1)(x+2)(2x-7)²= 0, we get roots
x = -2, 1, 3.5
We need to consider the following 4 intervals:
(−∞; −2), [−2; 1], (1; 3.5), (3.5; ∞)
1st interval (−∞; −2)
The expression (x-1)(x+2)(2x-7)² is positive as two of the multiples are negative and one is always positive (square number), and therefore does not satisfy the inequality.
2nd interval [−2; 1]
The expression is negative as only one of the multiples is negative, and therefore the interval (−1; 2) satisfies the inequality.
3rd interval (1; 3.5)
The expression is positive as all the multiples are positive. Therefore, the interval (1; 3.5) also does not satisfy the inequality.
4th interval
The expression is positive as above, and therefore also does not satisfy the inequality.
