Math Doubts

Roots of Quadratic Equation

The solutions of quadratic equation are called the roots of quadratic equation.

Quadratic equation is a second degree polynomial. So, it should have two solutions and they are called as the roots of a quadratic equation. The roots of quadratic equation are actually obtained by equating the quadratic expression to zero.

$ax^2+bx+c = 0$ is a quadratic equation in standard algebraic form and the solutions are simply denoted by the below quadratic formula.

$x \,=\, \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}$


The two roots of a quadratic equation are usually represented by alpha ($\alpha$) and beta ($\beta$) symbols in mathematics.

$(1)\,\,\,\,\,\,\,$ $\alpha \,=\, \dfrac{-b + \sqrt{b^2 -4ac}}{2a}$

$(2)\,\,\,\,\,\,\,$ $\beta \,=\, \dfrac{-b -\sqrt{b^2 -4ac}}{2a}$

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