# Thread: Solve the Polynomial Inequality

1. ## Solve the Polynomial Inequality

I threw this equation into Mathway, but the answer wasn't correct. I have two tries at the question, so looking for some help. The equation is as follows:

(x-10)(x+3)(x-2)^2 < 0

Any suggestions?

2. ## Re: Solve the Polynomial Inequality

Hey AceBoogie.

Hint: Try looking at values left and right of the zeroes (i.e. 10, -3, and 2) and see when you get a negative or a positive answer.

Then use this to get the regions when < 0 and you're done. (For example if f(x) = (x-10)(x+3)(x-2)^2 and f(1) < 0 then the interval [-3,2] is <= 0 since 1 is between -3 and 2).

3. ## Re: Solve the Polynomial Inequality

I think I am trying to set up the equation so the x values will make the equation = 0. In this case would the answer be:

(-3,2)U(2,10)?

4. ## Re: Solve the Polynomial Inequality

Originally Posted by AceBoogie
I threw this equation into Mathway, but the answer wasn't correct. I have two tries at the question, so looking for some help. The equation is as follows:

(x-10)(x+3)(x-2)^2 < 0
I have a different take on this.

Because $(x-2)^2\ge 0$ the only case we cannot have x=2 .

So we need $(x-10)(x+3)<0$ with $x\ne 2$