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Questions and Answers
Questions and Answers
What is the standard form of a quadratic equation?
What is the standard form of a quadratic equation?
- $ax + bx^2 = c$
- $ax^2 + bx = c$
- $ax^2 + bx + c = 0$ (correct)
- $x^2 + ax + bx = c$
What are the coefficients of a quadratic equation?
What are the coefficients of a quadratic equation?
- The first coefficient, the second coefficient, and the third coefficient
- The leading coefficient, the middle term coefficient, and the constant term coefficient
- The quadratic coefficient, the linear coefficient, and the constant coefficient (correct)
- The primary coefficient, the secondary coefficient, and the tertiary coefficient
How many solutions can a quadratic equation have?
How many solutions can a quadratic equation have?
- At most one solution
- At most two solutions (correct)
- Exactly two solutions
- At least two solutions
What is the quadratic formula used for?
What is the quadratic formula used for?
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What kind of roots does a quadratic equation always have?
What kind of roots does a quadratic equation always have?
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Questions and Answers
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Study Notes
Study Notes
Standard Form of a Quadratic Equation
- A quadratic equation is expressed in standard form as ax² + bx + c = 0, where a, b, and c are constants.
- The variable x represents the unknown, while a cannot be zero (a ≠ 0).
Coefficients of a Quadratic Equation
- The coefficients a, b, and c are numerical factors in the equation:
- a: Coefficient of x², determines the parabola's direction and width.
- b: Coefficient of x, influences the location of the vertex along the x-axis.
- c: Constant term, represents the y-intercept of the parabola.
Number of Solutions
- A quadratic equation can have two, one, or zero solutions.
- The number of solutions is determined by the discriminant (b² - 4ac):
- Two distinct solutions if the discriminant is positive.
- One repeated solution if it is zero.
- No real solutions if it is negative.
Quadratic Formula
- The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).
- It is used to find the solutions (roots) of a quadratic equation by substituting the coefficients.
Roots of a Quadratic Equation
- A quadratic equation always has two roots, considering complex numbers.
- The nature of the roots (real or complex) depends on the discriminant:
- Positive discriminant results in two distinct real roots.
- Zero discriminant results in one double root (real).
- Negative discriminant results in two complex roots.
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