Solving Quadratic equations by factoring

Front

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.

Front

What does it mean to factor a quadratic equation?

Back

Factoring a quadratic equation means rewriting it as a product of two binomials, such as (x - p)(x - q) = 0, where p and q are the solutions of the equation.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

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What are the solutions of a quadratic equation?

Back

The solutions of a quadratic equation are the values of x that make the equation true, often found by factoring, completing the square, or using the quadratic formula.

Front

How do you find the factors of x² + 2x - 3?

Back

To factor x² + 2x - 3, look for two numbers that multiply to -3 and add to 2. The factors are (x - 1)(x + 3).

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What is the first step in solving x² + 6x - 13 = 3?

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The first step is to make it equal to 0 by subtracting 3 from both sides, resulting in x² + 6x - 16 = 0.

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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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What are the roots of the equation 8n² + 10n - 3 = 0?

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The roots are n = 1/4 and n = -3/2.

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What does it mean if a quadratic equation has no real solutions?

Back

If a quadratic equation has no real solutions, it means the discriminant (b² - 4ac) is less than 0, indicating that the graph does not intersect the x-axis.

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How do you check if your factors are correct?

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You can check if your factors are correct by expanding them back to the original quadratic equation.