Question

When solved using the quadratic formula, the solutions to the equation $3x^2-4x-6=0$, rounded to the nearest hundredth, are

• A. $2.46,-3.79$
• B. $2.23,-0.90$
• C. $3.79,-2.46$
• D. $0.90,-2.23$

Answer 1

The correct option is B $2.23,-0.90$

$\Rightarrow$ Given quadratic equation is $3x^2-4x-6=0$, comparing it with $a{x}^2+bx+c=0$

$\Rightarrow$ We get, $a=3,b=-4,c=-6$

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

$=\frac{-(-4)\pm \sqrt{(-4{)}^2-4(3\left)\right(-6)}}{2\left(3\right)}$

$=\frac{4\pm \sqrt{16+72}}{6}$

$=\frac{4\pm \sqrt{88}}{6}$

$=\frac{4\pm 2\sqrt{22}}{6}$

$=\frac{2\pm \sqrt{22}}{3}$

$=\frac{2\pm 4.69}{3}$

$\Rightarrow$ $x=\frac{2+4.69}{3}$ and $x=\frac{2-4.69}{3}$

$\therefore$ $x=2.23$ and $x=-0.90$