Question

Find the roots of the quadratic equation $6x^2-13x+6=0$ by using the quadratic formula.

• A. $\frac{4}{3},\frac{3}{2}$
• B. $\frac{2}{3},\frac{7}{2}$
• C. $\frac{2}{5},\frac{3}{2}$
• D. $\frac{2}{3},\frac{3}{2}$

Answer 1

The correct option is D

$\frac{2}{3},\frac{3}{2}$

Given equation is $6x^2-13x+6=0$
On comparing with $a{x}^2+bx+c=0$, we get
a = 6, b = -13 and c = 6
By quadratic formula, $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
$=\frac{-(-13)\pm \sqrt{(-13{)}^2-4(6\left)\right(6)}}{2\left(6\right)}=\frac{13\pm \sqrt{169-144}}{12}=\frac{13\pm \sqrt{25}}{12}=\frac{13\pm 5}{12}=\frac{18}{12},\frac{8}{12}=\frac{2}{3},\frac{3}{2}$