solve the inequality

[maggie0160]

Solve the inequality x3 - 7x + 6 < 0

a. (-oo, 1) and (2, 3)
b. (1, 2) and (3, oo)
c. (-3, 1) and (2, oo)
d. (-oo, -3) and (1, 2)
e. (-oo, -3) and (-2, 1)
f. (-3, -2) and (1, oo)
g. none of these

I know d is not correct, I am confused about my signs. How do I know which is negative and postive?

 

[Unco]

Did you factorise it to get:
(x+3)(x-1)(x-2) < 0?

It is a cubic with three roots (where it cuts the x-axis). We want to know when it is below the x-axis.

The coefficient of x^3 is 1 which is positive and the curve crosses the x-axis three times so it must go up to the first root of x=-3, then come back down to x=1 and then back up to x=2.

It is below the x-axis as is comes up to x=-3, and when it is between x=1 and x=2.

So the intervals are (-oo, -3) and (1,2)