Solve The Quadratic Inequality 2x2 9x 7 0

So, I was talking to a friend the other day, and they mentioned that they were struggling with quadratic inequalities in their math class. I have to admit, my first reaction was "oh boy, those can be a real pain!" But then I started thinking, why not write about it and hopefully help my friend (and you, dear reader) understand it better? After all, math isn't that scary, right?

Now, let's dive into the problem at hand: 2x^2 + 9x + 7 = 0. This is a quadratic equation, and to solve the inequality, we need to find the values of x that make the equation true. I know, it sounds simple, but trust me, it can get tricky.

The Basics

So, to solve a quadratic inequality, we need to factor the equation, if possible. In this case, we have 2x^2 + 9x + 7 = 0, which can be factored as (2x + 7)(x + 1) = 0. Now we're getting somewhere!

Now, we need to find the values of x that make each factor equal to zero. This is where it gets interesting. We set each factor equal to zero and solve for x: 2x + 7 = 0 and x + 1 = 0. Simple, right?

Solving for x

Solving for x, we get x = -7/2 and x = -1. These are the critical points that divide the number line into intervals where the inequality is either true or false. Think of it like a mathematical puzzle!

Now, we need to test each interval to see where the inequality is true. This is the fun part! We can pick a value from each interval and plug it into the original equation to see if it's true. If it is, then the inequality is true for that entire interval.

And that's it! We've solved the inequality. I hope this helps you (and my friend) understand quadratic inequalities better. Remember, practice makes perfect, so don't be afraid to try out a few more examples on your own.