Mathematics
The Quadratic Formula
The quadratic formula x = (-b ± √(b² - 4ac)) / 2a solves every quadratic equation, even the ones that don't factor. Plug in a, b, and c — the rest is arithmetic.
How to Approach The Quadratic Formula
Identify a, b, c
Rewrite your equation as ax² + bx + c = 0. The coefficient on x² is a, on x is b, and the constant is c.
Compute the discriminant
b² - 4ac. This tells you how many real roots there are before you continue.
Plug into the formula
Substitute a, b, c into x = (-b ± √(b² - 4ac)) / 2a and simplify. You get two solutions, one with + and one with -.
Frequently Asked Questions
Why does the quadratic formula work?+
It's derived by completing the square on the general form ax² + bx + c = 0. Every quadratic, once rearranged, fits the same pattern.
What if b² - 4ac is negative?+
The roots are complex. Write them as (-b ± i√(4ac - b²)) / 2a. ScanSolve shows the complex roots automatically.
Is there a faster method?+
If the quadratic factors with small integers, factoring is faster. If a = 1 and you spot two numbers that multiply to c and add to b, use those. Otherwise, the formula always works.
Related Topics
More step-by-step guides in Mathematics and adjacent subjects.
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