Is a root the input or the solution for the quadratic formula?

Question

For the quadratic formula, what is a root - is it the numbers you put into it (a, b or c) or is it the answers you get after crunching the numbers (x1, x2)?

Answer 1

$x_1$ and $x_2$ are the roots of a quadratic equation.

In general, we say $x$ is a root of a function $f$ if $f(x)=0$.

Answer 2

The numbers $a,b,c$ in the quadratic polynomial $ax^2+bx+c$ are called coefficients, any value of $x$ for which the polynomial evaluates to $0$ is called a root of the polynomial

Answer 3

Your question is pretty much unclear. But I will try to answer what it is. You have a quadratic equation:

$$ax^2 + bx + c = 0 $$

Here, $a$, $b$ and $c$ are called the co-efficients of the equation.

And the quadratic formula gives you two values for $x$ , let's say $x_1$ and $x_2$. These are the roots or solutions of the quadratic equation, which means that putting these values in place of $x$ in the equation, would satisfy the equation. So in short:

$$a(x_1)^2 + bx_1 + c = 0 $$ $$a(x_2)^2 + bx_2 + c = 0 $$