The question asks whether the quadratic formula can be used to solve any quadratic equation. Let's break this down:

The quadratic formula is:

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

This formula can solve any equation of the form $ax^2 + bx + c = 0$, which is a quadratic equation.

The quadratic formula works for all quadratic equations, even when the discriminant ($b^2 - 4ac$) is:

1. Positive: Two real solutions.
2. Zero: One real solution (a double root).
3. Negative: Two complex (non-real) solutions.

Thus, the correct answer to the question is True, because the quadratic formula is always applicable, regardless of the discriminant's value.

Would you like more details on this, or have any other questions?

Here are 5 related questions for deeper understanding:

1. What is the discriminant and how does it affect the nature of the solutions of a quadratic equation?
2. Can the quadratic formula be derived from completing the square?
3. How do you apply the quadratic formula when the discriminant is negative?
4. What is the significance of the quadratic formula in real-world applications?
5. Are there any conditions where solving a quadratic equation by factoring is more efficient than using the quadratic formula?

Tip: Always check the value of the discriminant to determine the type of solutions you can expect from a quadratic equation!