The quadratic formula is a solution for finding the roots of a quadratic equation of the form:

$ax^2 + bx + c = 0$

where:

• $a$, $b$, and $c$ are constants, and
• $a \neq 0$ (since the equation would not be quadratic if $a = 0$).

The formula is:

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

Explanation:

• Discriminant ($b^2 - 4ac$): This part under the square root determines the nature of the roots.
  • If $b^2 - 4ac > 0$, there are two distinct real roots.
  • If $b^2 - 4ac = 0$, there is exactly one real root (a repeated root).
  • If $b^2 - 4ac < 0$, there are two complex roots.

The $\pm$ symbol means there are two solutions for $x$, calculated by adding and subtracting the square root of the discriminant.

Would you like more details or have any specific questions?

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Related Questions:

1. How is the discriminant used to determine the nature of the roots?
2. What are some real-life applications of the quadratic formula?
3. How can we derive the quadratic formula by completing the square?
4. Why does the formula not work if $a = 0$?
5. How is the quadratic formula used in solving equations in physics?

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Tip: Memorize the quadratic formula by practicing with different values of $a$, $b$, and $c$.