Question

Ramiya is using the quadratic formula to solve a quadratic equation. Her equation is x = StartFraction negative 3 plus or minus StartRoot 3 squared minus 4(1)(2) EndRoot Over 2(1) EndFraction after substituting the values of a, b, and c into the formula. Which is Ramiya’s quadratic equation? Quadratic formula: x = StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction

Answer 1

Explanation:

Somebody (possibly in seventh-century India) was solving a lot of quadratic equations by completing the square. At some point, he (and, yes, it would have been a guy back then) noticed that he was always doing the exact same steps in the exact same order for every equation.

The great power of algebra is that it provides us with the ability to deal with abstractions, such as formulas that always work. This can relieve us from the burden and messiness of having to muck about with the numbers every single time we do the exact same thing. Using this power with respect to solving quadratics by completing the square, he made a formula out of what he'd been doing; namely, the Quadratic Formula, which states:

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