Equations · Algebra and geometry
Quadratic formula
The two solutions of any quadratic equation ax² + bx + c = 0, from its three coefficients.
x = (−b ± √(b² − 4ac)) / 2a
Aethel says
x equals the quantity negative b plus or minus the square root of the quantity b squared minus 4 a c, over 2a
What it says
Every equation of the form a x squared plus b x plus c equals zero, with a not zero, is solved by this formula. The plus or minus sign gives the two solutions.
The part under the square root, b squared minus 4ac, is the discriminant. When it is positive there are two real solutions, when it is zero there is one, and when it is negative the two solutions are complex numbers.
Symbol by symbol
| Symbol | Say it | Means |
|---|---|---|
| x | x | the unknown being solved for |
| a, b, c | a, b, c | the coefficients of x squared, of x, and the constant term |
| ± | plus or minus | one solution takes the plus, the other the minus |
| √ | the square root of | the number that, squared, gives what is underneath |
More on±Plus or minus√Square root
Where you meet it
Algebra courses, physics problems about projectiles, and anywhere a parabola meets a line.
Questions
How do you say Quadratic formula out loud?
x = (−b ± √(b² − 4ac)) / 2a is read: “x equals the quantity negative b plus or minus the square root of the quantity b squared minus 4 a c, over 2a.” That is exactly what Aethel says when it meets the formula in a book.
What does x mean in Quadratic formula?
x (said “x”) is the unknown being solved for.
What does a, b, c mean in Quadratic formula?
a, b, c (said “a, b, c”) is the coefficients of x squared, of x, and the constant term.
Can I listen to the equations in my own textbook like this?
Yes. Upload a PDF, EPUB or text file and Aethel reads it aloud with every equation spoken as maths, the way it reads this one, and highlights each sentence as it goes. You can start free.