SOLUTION: Hi. I have been trying for over an hour and can not solve the following polynomial inequality. {{{ x^2+5x<=3 }}} Correct answer is given: [-3,1] Thank you in advance

You can put this solution on YOUR website!

Solve it as equal, then add the <

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=37 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.54138126514911, -5.54138126514911. Here's your graph:

Sub <= for the equal signs.
All values between the 2 solutions fit the inequality.
----------------
----------------
It's not -3 and 1.
For the solution to be -3 and 1:

--> -3>=x>=1