Roots of a Quadratic function

Definition

The value of a variable that makes the quadratic function zero is called its root.

What is the Root of a Quadratic function?

A value can be substituted in the place of variable of a quadratic function to find its value. The quadratic function is equal to zero in some cases. So, the substituting value is called the root of a quadratic function. It is also called the zero of a quadratic function.

The highest exponent of a variable in a quadratic function is $2$. So, a quadratic function always has two roots (or zeros). So, let’s learn more about the roots of a quadratic function.

The above simple example helped you to understand what the roots of a quadratic function really are.

Actually, it is not always easy to guess the roots of a quadratic function. So, we require a special formula to find the roots of a quadratic function easily.

Formula to find the Roots

The roots of a quadratic function are denoted by alpha and beta in mathematics. The substitution of zeros $\alpha$ and $\beta$ in the place of variable makes quadratic function $ax^2+bx+c$ zero.

$(1).\,\,$ $a\alpha^2+b\alpha+c = 0$

$(2).\,\,$ $a\beta^2+b\beta+c = 0$

The following are the values of two solutions of a quadratic equation in general form.

$\therefore \,\,\,\,\,\,$ $\alpha \,=\, \dfrac{-b+\sqrt{b^2-4ac}}{2a}$ $\,\,\,$ or $\,\,\,$ $\beta \,=\, \dfrac{-b-\sqrt{b^2-4ac}}{2a}$

Now, they can be used as formulas to find the roots of a quadratic function in mathematics.

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