Ace Algebra 2025 – Your Ultimate Equation Adventure Awaits!

The correct quadratic formula is derived from the standard form of a quadratic equation, which is \( ax^2 + bx + c = 0 \). To find the solutions for \( x \), we use the quadratic formula:

\[

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

\]

In this formula:

- The term \(-b\) indicates that we take the opposite of the coefficient of the \(x\) term (which is \(b\)).

- The square root expression, \(\sqrt{b^2 - 4ac}\), represents the discriminant. This part determines the nature and number of solutions:

- If the discriminant is positive, there are two distinct real solutions.

- If it is zero, there is exactly one real solution (a repeated root).

- If it is negative, the solutions are complex.

- Finally, the entire expression is divided by \(2a\), where \(a\) is the coefficient of the \(x^2\) term.

This structure captures essential features of how to solve any quadratic equation. The first choice clearly outlines the correct form, including the necessary signs and operations.

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