Adv Algebra Trig H Question

Question

Two questions

 

1) I am confused about how to solve the inequality: x^3-x^2+3<0. My math book has the answer (-infinity, 1.86), but I have absolutely no clue how to do that. 

 

2) How would you find the zero of 5x^3-18x^2-35x=0. I got to the factoring part, but don't know what to do after that. 

 

Thank you!

Answer 1

1.  The answer in your book is not correct.  For example, when x = 0, x³ - x² + 3 > 0.

 

2.  5x³ - 18x² - 35x = 0

 

     x(5x² - 18x - 35) = 0

 

     x(5x + 7)(x - 5) = 0    So, x = 0, -7/5, 5