What is the quadratic formula and how do I use it?

What is the quadratic formula?

The quadratic formula is used to find the solutions of a quadratic equation, which is in the form ax² + bx + c = 0. It is given by the formula: x = (-b ± √(b² - 4ac)) / (2a).

Can you explain how to use the quadratic formula with an example?

Sure! Let's say we have the equation 2x² + 3x - 5 = 0. Here, a = 2, b = 3, and c = -5. Plugging these values into the formula gives us x = (-3 ± √(3² - 42(-5))) / (2*2).

What do I do after calculating the discriminant?

After calculating the discriminant (b² - 4ac), you determine if it's positive, negative, or zero. A positive discriminant means two real solutions, zero means one real solution, and negative means no real solutions.

Can you show me the final steps to solve the example?

Absolutely! For our example, the discriminant is 49, so we have x = (-3 ± 7) / 4. This gives us two solutions: x = 1 and x = -2.5.