Math Doubts

Roots of Quadratic Equation

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

Quadratic equation is a second degree polynomial. So, It can be derived that the quadratic equation has two solutions when the quadratic expression equals to zero.

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

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


The two roots of quadratic equation are usually represented by alpha and beta symbols.

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

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

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