Question

Solve the following quadratic equation using quadratic formula: $9x^2-9x+2=0$

• A. $\{\frac{2}{3},\frac{1}{3}\}$
• B. $\{\frac{2}{3},\frac{-1}{3}\}$
• C. $\{\frac{-2}{3},\frac{1}{3}\}$
• D. None of these

Answer 1

Answer: (A)

$\{\frac{2}{3},\frac{1}{3}\}$

$\Rightarrow$ The given quadratic equation is $9x^2-9x+2=0$, comparing it with $a{x}^2+bx+c=0$

$\Rightarrow$ We get, $a=9,b=-9,c=2$

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

$=\frac{-(-9)\pm \sqrt{(-9{)}^2-4(9\left)\right(2)}}{2\left(9\right)}$

$=\frac{9\pm \sqrt{81-72}}{18}$

$=\frac{9\pm \sqrt{9}}{18}$

$=\frac{9\pm 3}{18}$

$=\frac{3\pm 1}{6}$

$\Rightarrow$ $x=\frac{3+1}{6}$ and $x=\frac{3-1}{6}$

$\therefore$ $x=\frac{2}{3}$ and $x=\frac{1}{3}$