Solving Quadratic Equations

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What is a quadratic equation?

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A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

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What are the methods to solve quadratic equations?

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The main methods to solve quadratic equations include factoring, using the quadratic formula, completing the square, and graphing.

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What is the Quadratic Formula?

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The Quadratic Formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation.

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How do you factor a quadratic equation?

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To factor a quadratic equation, express it in the form (x - p)(x - q) = 0, where p and q are the roots of the equation.

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What is a perfect square trinomial?

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A perfect square trinomial is a quadratic expression that can be written as the square of a binomial, such as (x - a)² = x² - 2ax + a².

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What does it mean to solve by factoring?

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Solving by factoring involves rewriting the quadratic equation as a product of its factors and then setting each factor equal to zero to find the solutions.

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What is the significance of the discriminant in the Quadratic Formula?

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The discriminant, given by b² - 4ac, determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

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How do you complete the square for a quadratic equation?

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To complete the square, rearrange the equation to isolate the constant term, then add and subtract the square of half the coefficient of x, allowing you to express it as a perfect square.

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What is the GCF (Greatest Common Factor) and how is it used in factoring?

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The GCF is the largest factor that divides all terms in a polynomial. It is used in factoring to simplify the expression before applying other factoring techniques.

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What are the roots of a quadratic equation?

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The roots of a quadratic equation are the values of x that satisfy the equation, which can be found using various methods such as factoring or the quadratic formula.