Question

The roots of the following quadratic equation (if they exist) by the method of completing the square.
$3x^2$ + 11x + 10 = 0

are$-\frac{5}{3}$, $-2$

• A. True
• B. False

Answer 1

The correct option is A True

$3x^2+11x+10=0$

$\Rightarrow$ $x^2+\frac{11}{3}x+\frac{10}{3}=0$

$\Rightarrow$ Here, $a=1,b=\frac{11}{3},c=\frac{10}{3}$

$\Rightarrow$ $x^2+\frac{11}{3}x=-\frac{10}{3}$

${\left(\frac{-b}{2a}\right)}^2={\left(\frac{-\frac{11}{3}}{2\left(1\right)}\right)}^2=\frac{121}{36}$

Adding $\frac{121}{36}$ on both sides,

$\Rightarrow$ $x^2+\frac{11}{3}x+\frac{121}{36}=-\frac{10}{3}+\frac{121}{36}$

$\Rightarrow$ ${(x+\frac{11}{6})}^2=\frac{1}{36}$

$\Rightarrow$ $x+\frac{11}{6}=\pm \frac{1}{6}$

$\Rightarrow$ $x+\frac{11}{6}=\frac{1}{6}$ and $x+\frac{11}{6}=-\frac{1}{6}$

$\Rightarrow$ $x=-\frac{5}{3}$ and $x=-2$

$\Rightarrow$ We can see, roots given in question are correct.