SOLUTION: What are the negative and positive intervals to these equations? y=x^2+5x+6 y=2x^2-11x-5

1.  y = .


    Find the roots of the polynomial. For it, factorize the polynomial:

     = (x+2)*(x+3).

    So, the roots are x = -3  and  x = -2.

    The polynomial is negative when  -3 < x < -2, i.e in the interval (-3,-2).

    The polynomial is positive when  x < -3  or  x > -2, i.e. in the the union of two semi-infinite intervals  (,) U (,).


2.  Now make the same with the second equation.

    First find its roots (you can use the quadratic formula).

    Then analyse the sign of the polynomial between the roots, to the left of the roots and to the right of the roots.