When it comes to solving second degree , it can seem daunting at first, but with some practice and patience, anyone can learn how to them. In this article, we’ll be discussing the steps to solving a second degree .

Step 1: Simplify the inequality

The first step in solving a second degree inequality is to simplify the inequality by getting all the terms to one side. In other words, you want to put all the terms with the variable on one side and all the constant terms on the other.

For example, take the inequality x^2 – 4x + 3 < 0. To simplify this inequality, we first need to move all the terms to the left-hand side: x^2 - 4x + 3 - 0 < 0 x^2 - 4x + 3 < 0 Now we have simplified the inequality and can move on to the next step. Step 2: Factor the quadratic expression The second step in solving a second degree inequality is to factor the quadratic expression. In order to factor the quadratic expression, we need to find two numbers that add up to -4 and multiply to 3. These numbers are -1 and -3, so we can write the quadratic expression as: (x - 1)(x - 3) < 0 Step 3: Determine the sign of each factor The third step in solving a second degree inequality is to determine the sign of each factor. We do this by looking at each factor and determining whether it is positive or negative. We know that (x - 1) and (x - 3) are both negative when x < 1 and x < 3, respectively. Likewise, we know that they are both positive when x > 3 and x > 1, respectively. Therefore, we can create a sign chart:

(x – 1)(x – 3) < 0 --------------------- x < 1 x > 3

– + + +

Step 4: Determine the solution

The fourth and final step in solving a second degree inequality is to determine the solution. We do this by looking at the sign chart and determining when the function is negative.

(x – 1)(x – 3) < 0 --------------------- x < 1 x > 3

– + + +

We see that the function is negative when x is between 1 and 3. Therefore, the solution to the inequality is:

1 < x < 3 In conclusion, solving a second degree inequality involves simplifying the inequality, factoring the quadratic expression, determining the sign of each factor, and determining the solution. With enough practice and determination, anyone can learn how to solve these types of inequalities.

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