Quadratic Formula!!!

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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 ax² + bx + c = 0.

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What does the discriminant in the quadratic formula indicate?

Back

The discriminant (b² - 4ac) indicates the nature of the roots of the quadratic equation: if positive, there are two distinct real solutions; if zero, there is one real solution; if negative, there are two complex solutions.

Front

How do you solve a quadratic equation using the quadratic formula?

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To solve a quadratic equation using the quadratic formula, identify coefficients a, b, and c from the equation ax² + bx + c = 0, then substitute them into the formula x = (-b ± √(b² - 4ac)) / (2a) to find the values of x.

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What is the significance of a positive discriminant?

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A positive discriminant indicates that the quadratic equation has two distinct real solutions.

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What is the significance of a zero discriminant?

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A zero discriminant indicates that the quadratic equation has exactly one real solution, also known as a repeated or double root.

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What is the significance of a negative discriminant?

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A negative discriminant indicates that the quadratic equation has no real solutions, but two complex solutions.

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How can you determine the number of solutions for a quadratic equation?

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You can determine the number of solutions by calculating the discriminant (b² - 4ac): if it's positive, there are two solutions; if zero, one solution; if negative, no real solutions.

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What is the first step in solving the equation x² - 2x - 8 = 0 using the quadratic formula?

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The first step is to identify the coefficients a, b, and c from the equation, which are a = 1, b = -2, and c = -8.

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How do you find the roots of the equation 3 + 9r² = 12?

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First, rearrange the equation to 9r² = 12 - 3, then simplify to 9r² = 9, and finally take the square root to find r = ±1.

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What is the value of the discriminant for the equation 3k² + k - 1 = 0?

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The value of the discriminant is 13, calculated using the formula b² - 4ac, where a = 3, b = 1, and c = -1.