key term - ±

Definition

The symbol '±' is a mathematical symbol that represents the concept of 'plus or minus'. It is used to indicate that a value or expression can have two possible solutions, one positive and one negative. This symbol is commonly encountered in the context of solving equations and working with polynomial expressions.

5 Must Know Facts For Your Next Test

1. The '±' symbol is used to represent the two possible solutions to a quadratic equation, one positive and one negative.
2. When solving a quadratic equation using the square root property, the '±' symbol is used to indicate the two possible solutions.
3. In the context of factoring polynomials, the '±' symbol is used to represent the two possible signs (positive or negative) of the factors.
4. The '±' symbol is often used in the quadratic formula, which is a formula used to solve any quadratic equation.
5. The '±' symbol is also used in the context of radical expressions, where it indicates the two possible solutions for the square root of a number.

Review Questions

• Explain how the '±' symbol is used in the context of solving quadratic equations using the square root property.
  • When solving a quadratic equation using the square root property, the '±' symbol is used to indicate the two possible solutions. The square root property states that if $x^2 = a$, then $x = \pm \sqrt{a}$. This means that there are two possible values for $x$, one positive and one negative. The '±' symbol is used to represent these two solutions, allowing the equation to be written in the form $x = \pm \sqrt{a}$.
• Describe the role of the '±' symbol in the context of factoring polynomials.
  • In the context of factoring polynomials, the '±' symbol is used to represent the two possible signs (positive or negative) of the factors. When factoring a polynomial expression, the '±' symbol is often used to indicate the two possible combinations of signs for the factors. For example, if a polynomial expression can be factored as $(x + 3)(x - 2)$, the '±' symbol would be used to represent the two possible factors: $(x \pm 3)(x \mp 2)$.
• Analyze the significance of the '±' symbol in the quadratic formula and its relationship to the solutions of a quadratic equation.
  • The quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, is a formula used to solve any quadratic equation of the form $ax^2 + bx + c = 0$. The '±' symbol in the quadratic formula represents the two possible solutions to the equation, one positive and one negative. This is because the square root term, $\sqrt{b^2 - 4ac}$, can have two possible values, leading to two possible solutions for $x$. The '±' symbol allows the formula to capture both solutions in a concise way, highlighting the fact that quadratic equations can have two distinct real number solutions.

Related terms

Quadratic Equation:

A polynomial equation of the form $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are real numbers and $a \neq 0$.

Square Root Property:

A method for solving quadratic equations by taking the square root of both sides of the equation.

Factoring:

The process of expressing a polynomial as a product of simpler polynomial expressions.