Math Problem Statement

What is the quadratic formula?

A. x = [-b ± sqrt(b^2 - 4ac)] / 2a

B. x = [-b ± sqrt(a^2 - 4bc)] / 2a

C. x = [-a ± sqrt(b^2 - 4ac)] / 2b

D. x = [-b ± sqrt(b^2 - 4ab)] / 2c

Solution

The correct form of the quadratic formula is:

A. x=b±b24ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

This formula is used to solve quadratic equations of the form ax2+bx+c=0ax^2 + bx + c = 0, where:

  • aa, bb, and cc are coefficients.
  • ±\pm means there are two solutions: one with a plus and one with a minus.
  • The expression b24acb^2 - 4ac is called the discriminant, which determines the nature of the roots.

Would you like more details on how to apply this formula or any specific example?

Here are 5 related questions:

  1. How do you use the discriminant to determine the number of solutions?
  2. What are the possible types of roots based on the discriminant?
  3. Can the quadratic formula be used for any quadratic equation?
  4. What happens if the discriminant is negative?
  5. How do you derive the quadratic formula?

Tip: Always check the value of the discriminant before calculating the roots to know if they are real or complex.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Discriminant

Formulas

Quadratic formula: x = [-b ± sqrt(b^2 - 4ac)] / 2a

Theorems

Quadratic formula theorem

Suitable Grade Level

Grades 9-11