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Questions and Answers
In a quadratic equation expressed in the standard form $ax^2 + bx + c = 0$, which of the following statements is correct regarding the coefficients?
In a quadratic equation expressed in the standard form $ax^2 + bx + c = 0$, which of the following statements is correct regarding the coefficients?
- The coefficient 'c' cannot be zero, but 'a' and 'b' can be zero.
- The coefficient 'a' can be zero, but 'b' cannot be zero.
- The coefficient 'a' cannot be zero, while 'b' and 'c' can be zero. (correct)
- The coefficients 'a', 'b', and 'c' must all be non-zero.
The degree of any quadratic polynomial is always 3.
The degree of any quadratic polynomial is always 3.
False (B)
Write any quadratic equation in standard form where 'a' equals 1, 'b' equals -5, and 'c' equals 6.
Write any quadratic equation in standard form where 'a' equals 1, 'b' equals -5, and 'c' equals 6.
x² - 5x + 6 = 0
A quadratic equation is defined as P(x) = 0, where P(x) is a polynomial of degree _____.
A quadratic equation is defined as P(x) = 0, where P(x) is a polynomial of degree _____.
Match the coefficient from a quadratic equation in the standard form $ax^2 + bx + c = 0$ with its description:
Match the coefficient from a quadratic equation in the standard form $ax^2 + bx + c = 0$ with its description:
Flashcards
Quadratic Polynomial Form
Quadratic Polynomial Form
ax² + bx + c, where 'a' is not zero.
Standard Quadratic Equation
Standard Quadratic Equation
ax² + bx + c = 0, where a ≠ 0.
What 'a' Represents
What 'a' Represents
Coefficient of the x² term.
Quadratic Equation Definition
Quadratic Equation Definition
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Field Area Equation
Field Area Equation
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Study Notes
Quadratic Polynomials and Equations
- Quadratic polynomials have a general form of ax² + bx + c, where 'a' is not equal to zero
- The degree of a quadratic polynomial is 2
- A quadratic equation is formed when a quadratic polynomial is set equal to zero
- The general or standard form of a quadratic equation is ax² + bx + c = 0, where a ≠ 0
- In the standard form, a, b, and c are real numbers
Coefficients in Quadratic Equations
- 'a' is the coefficient of x²
- 'b' is the coefficient of x
- 'c' is the constant term
- It is acceptable for 'b' to be zero, but 'a' must never be zero to maintain the quadratic nature
Definition
- A quadratic equation can be defined as P(x) = 0, where P(x) is a polynomial of degree 2
Real-Life Application
- Quadratic equations can be applied to real-life problems, such as constructing a rectangular field with specific area and length-width relationship
- For a rectangular field with an area of 7000 square meters, and the length being 30 meters more than the width, the quadratic equation is x² + 30x - 7000 = 0, where X is the width
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