Question

Find, using the quadratic formula, the roots of the following quadratic equation, if they exist.

(i). $3x^2-5x+2=0$

Answer 1

We know that, for equation $a{x}^2+bx+c=0$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ are roots of the equation,

Given equation is $3x^2-5x+2=0$

$a=3,b=-5$ and $c=2$

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

$=\frac{5\pm \sqrt{25-24}}{6}$

$=\frac{5\pm 1}{6}$

$\Rightarrow x=\frac{6}{6}$ or $\frac{4}{6}$

$\therefore x=1$ or $x=\frac{2}{3}$.