91Ó°ÊÓ

Quadratic equations are a type of polynomial equation that involves terms up to the second degree. The general form of a quadratic equation is \( ax^2 + bx + c = 0 \), where \( a \), \( b \), and \( c \) are constants. To solve these equations, you are finding the values of \( x \) (or another variable) that satisfy the equation. There are several methods to solve quadratic equations:

• Factoring
• Completing the square
• Quadratic formula
• Graphing

In this exercise, we specifically used the quadratic formula to find the solutions.

The quadratic formula is a powerful tool to solve any quadratic equation. It is derived from the process of completing the square and is given by:
\[ u = \frac{-b\begin{matrix}\bold{\textbf{±}}\bold{\textbf{\textbf{(}}}}\bold{\textbf{\textbf{\textbf{(}}}}}\bold{\textbf{\textbf{(}}}}\bold{\textbf{\textbf{(}}}}\textbf{√}}{b2 - 4ac}}}{2a} \]
This works for any quadratic equation of the form \( ax^2 + bx + c = 0 \). Here’s a step-by-step breakdown:

1. Identify the coefficients \( a \), \( b \), and \( c \) from the quadratic equation.
2. Substitute these values into the quadratic formula.
3. Calculate the discriminant \( b^2 - 4ac \). This value will determine the number and type of roots:

• Positive discriminant: Two real and distinct roots
• Zero discriminant: One real double root
• Negative discriminant: Two complex roots

4. Solve for \( x \) using the formula and simplify the expressions to get the roots.

Rounding numbers is an essential skill in mathematics to simplify numerical results, making them easier to read and understand. When rounding to the nearest hundredth, you look at the third digit after the decimal point:

• If the third digit is 5 or more, round the second digit up.
• If the third digit is less than 5, leave the second digit as is.

For example, if you have a number like 3.625:

• The third digit is 5, so round the second digit (2) up to 3.

Thus, 3.625 rounded to the nearest hundredth is 3.63.
Ensuring correct rounding is crucial when reporting final answers in exercises, as it reflects proper mathematical precision.