Solving Quadratic equations by the quadratic formula

A method of solving quadratic equations by using a formula is called quadratic formula method.

Method

$ax^2+bx+c = 0$ is a quadratic equation in standard algebraic form and the solution of the quadratic equation is,

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

The solution of the quadratic equation is used as a formula to solve the quadratics mathematically. Hence, the mathematical approach of solving quadratics by formula is called quadratic formula method.

Example

$3x^2 + 2x -5 = 0$ is a quadratic equation.

Compare this equation with standard form quadratic equation $ax^2 + bx + c = 0$. Therefore, $a = 3$, $b = 2$ and $c = -5$. Substitute them in the quadratic formula to learn how to solve any quadratic equation by the quadratic formula method.

$\implies x = \dfrac{-2 \pm \sqrt{2^2 -4 \times 3 \times (-5)}}{2 \times 3}$

$\implies x = \dfrac{-2 \pm \sqrt{4 + 60}}{6}$

$\implies x = \dfrac{-2 \pm \sqrt{64}}{6}$

$\implies x = \dfrac{-2 \pm 8}{6}$

$\implies x = \dfrac{-2 + 8}{6}$ and $x = \dfrac{-2 -8}{6}$.

$\implies x = \dfrac{6}{6}$ and $x = \dfrac{-10}{6}$.

$\,\,\, \therefore \,\,\,\,\,\, x = 1$ and $x = -\dfrac{5}{3}$.

By using the quadratic formula method, the roots of the quadratic equation $3x^2 + 2x -5 = 0$ are $1$ and $-\dfrac{5}{3}$.