Solving Quadratic and Polynomial Equations

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What is a quadratic equation?

Back

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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How do you solve a quadratic equation using factoring?

Back

To solve a quadratic equation by factoring, express it in the form (px + q)(rx + s) = 0, then set each factor to zero and solve for x.

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What is the quadratic formula?

Back

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

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What does the discriminant tell you about a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if > 0, two real solutions; if = 0, one real solution; if < 0, no real solutions.

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What is the vertex of a parabola?

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The vertex of a parabola is the highest or lowest point on the graph, found at the coordinates (h, k) in the vertex form y = a(x - h)² + k.

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How do you complete the square for a quadratic equation?

Back

To complete the square, rearrange the equation to isolate the x² term, add (b/2)² to both sides, and factor the left side.

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What is a polynomial?

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A polynomial is a mathematical expression consisting of variables raised to non-negative integer powers, combined using addition, subtraction, and multiplication.

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the expression.

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How do you simplify complex numbers?

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To simplify complex numbers, combine like terms, such as real parts and imaginary parts, and express in the form a + bi.

Front

What is the standard form of a quadratic equation?

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The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.