Roots, zeros, x-intercepts of a Quadratic Equation

A Quadratic Equation always has two solutions called the "roots" of the quadratic equation.

The root of a quadratic equation is also called :
  • Solutions of the quadratic equation
  • zeros of the quadratic polynomial
  • x-intercepts of the quadratic equation/function
Let us study why the roots of a quadratic equation have so many names:

1) Solutions of the quadratic equation:
The roots of a quadratic equation are the two values which we obtain after solving a quadratic equation, so naturally they are also called the solutions of the quadratic equation.
2) Zeros of the quadratic polynomial:
If we equate any quadratic polynomial or quadratic function to zero and then solve it, we get two equal or unequal values of x. These are thus called the zeros of the quadratic polynomial, since these values are obtained by equating that quadratic to zero.
3) X - intercepts of the quadratic equation/function:
The quadratic equation, quadratic polynomial, or quadratic function, when graphed on a two dimensional coordinate plane, intersects the x axis at most two points. The x coordinates at these two points are the two solutions/roots of the quadratic equation, and thus they are known as the x intercepts, as the quadratic polynomial intersects the x axis at those points.
The nature of the roots of a quadratic equation can be determined without actually calculating them. See the complete article on the "Nature of roots of a quadratic equation"

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