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

Question 235794: Hi.
I have been trying for over an hour and can not
solve the following polynomial inequality.

Correct answer is given: [-3,1]
Thank you in advance
Answer by Alan3354(69443) (Show Source): 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

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