Second degree s are commonly known as quadratic , which are of the form ax^2 + bx + c = 0. These equations require the determination of two different solutions – one positive and one negative. Solving a second degree equation can be tricky as it involves many mathematical operations, but with the right approach and a little practice, anyone can these equations without any difficulty.

Here are the steps to solve a second degree equation :

Step 1: Using the quadratic formula:

The quadratic formula is a foolproof method to solve quadratic equations. It states that if the equation is of the form ax^2 + bx + c = 0, then the solutions can be obtained using the formula -x = (-b ± √ b^2 – 4ac) / 2a.

Step 2: Determine the values of a, b, and c:

Before using the quadratic formula, the values of a, b, and c should be known. These values are the coefficients of x^2, x, and the constant term, respectively.

Step 3: Substitute the values of a, b, and c in the quadratic formula:

After calculating the values of a, b, and c, they must be put into the quadratic formula to obtain the values of x.

Step 4: Simplify the quadratic formula equation:

The formula will produce two values of x – one positive and one negative. These values should be simplified using the appropriate arithmetic methods to ensure that they are in their simplest form.

Step 5: Check your answers:

After calculating the two values of x, they should be tested and confirmed by substituting them back into the original equation. If the values of x satisfy the equation, then they are correct.

Example:

Let’s take the equation 2x^2 + 5x – 3 = 0 as an example, and solve it using the above method.

Step 1: Applying the quadratic formula:

-x = (-b ± √ b^2 – 4ac) / 2a, where a = 2, b = 5, and c = -3.

-x = (-5 ± √ (5^2 – 4 * 2 * -3)) / 4

Step 2: Simplifying the equation:

-x = (-5 ± √ 49) / 4

-x = (-5 + 7) / 4 or (-5 – 7) / 4

So, the two values of x are 1/2 and -3.

Step 3: Checking the answers:

Finally, we check these values by substituting them back into the original equation.

2 * (1/2)^2 + 5 * (1/2) – 3= 0
2 * (-3)^2 + 5 (-3) – 3 = 0

Hence, we can conclude that the solutions are correct.

In conclusion, solving a quadratic equation may seem daunting, but it is nothing more than a sequence of simple mathematical steps. The quadratic formula is one of the most useful and efficient methods for solving second degree equations. A little practice is all that is needed to master this technique.

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