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Questions and Answers
What type of numbers are not considered algebraic?
What type of numbers are not considered algebraic?
- Whole numbers like 2 and 7
- Transcendental numbers like π and e (correct)
- Rational numbers like 3/4 and 5
- Imaginary numbers like √(-1)
Which of the following is an algebraic expression?
Which of the following is an algebraic expression?
- π + e
- 3x^2 - 2xy + c (correct)
- 2^x + 3
- √(1-x^2)/(1+x^2)
What is a rational expression?
What is a rational expression?
- An expression with only addition and subtraction operations
- An expression involving transcendental numbers
- An expression that may be rewritten to a rational fraction using arithmetic properties (correct)
- An expression with irrational numbers
Which operation turns a square root into an algebraic expression?
Which operation turns a square root into an algebraic expression?
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What makes an equation algebraic?
What makes an equation algebraic?
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Study Notes
Non-Algebraic Numbers
- Transcendental numbers, such as π (pi) and e (Euler's number), are not algebraic.
- These numbers cannot be the roots of any non-zero polynomial equation with rational coefficients.
Algebraic Expressions
- An expression containing numbers, variables, and operations (such as addition or multiplication) is termed an algebraic expression.
- Example of an algebraic expression: 3x² + 5x - 7.
Rational Expressions
- A rational expression is a fraction where both the numerator and the denominator are polynomials.
- Example: (2x + 3) / (x² - 1) is a rational expression.
Square Root Operations
- The operation of squaring a number converts a square root into an algebraic expression.
- For instance, if y = √x, squaring both sides gives y² = x, forming an algebraic expression.
Characteristics of Algebraic Equations
- An equation is considered algebraic if it involves variables and can be expressed as a polynomial equation.
- For example, an equation like 2x + 3 = 7 is algebraic because it can be rearranged into polynomial form.
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