What is the quadratic formula used for solving ax² + bx + c = 0?

What is the quadratic formula used for solving ax² + bx + c = 0?

• A. x = (-b ± √(b² - 4ac)) / (2a)
• B. x = (-b ± √(4ac)) / 2a
• C. x = (b ± √(b² + 4ac)) / (2a)
• D. x = (b ± 4ac) / (2a)

Answer: (A)

The quadratic formula, represented as x = (-b ± √(b² - 4ac)) / (2a), is used to find the solutions or roots of the quadratic equation ax² + bx + c = 0. This formula allows us to determine the values of x that satisfy the equation, considering a, b, and c are coefficients where a is not equal to zero. In this formula, the term under the square root, b² - 4ac, is known as the discriminant. The discriminant plays a crucial role in determining the nature of the roots. If it is positive, there are two distinct real roots; if it is zero, there is one real root (a repeated root); and if it is negative, the roots are complex numbers. The structure of the quadratic formula is derived from completing the square, which rearranges the standard quadratic equation. The formula provides a systematic way to solve any quadratic equation, regardless of the specific values of the coefficients, making it crucial for various applications in algebra, science, and engineering.

The quadratic formula, represented as x = (-b ± √(b² - 4ac)) / (2a), is used to find the solutions or roots of the quadratic equation ax² + bx + c = 0. This formula allows us to determine the values of x that satisfy the equation, considering a, b, and c are coefficients where a is not equal to zero.

In this formula, the term under the square root, b² - 4ac, is known as the discriminant. The discriminant plays a crucial role in determining the nature of the roots. If it is positive, there are two distinct real roots; if it is zero, there is one real root (a repeated root); and if it is negative, the roots are complex numbers.

The structure of the quadratic formula is derived from completing the square, which rearranges the standard quadratic equation. The formula provides a systematic way to solve any quadratic equation, regardless of the specific values of the coefficients, making it crucial for various applications in algebra, science, and engineering.