Question

Say true or false:

The roots of $\frac{1}{2}{x}^2+\sqrt{11}x+1=0$ are $x=-14,-8$.

• A. True
• B. False

Answer 1

The correct option is B False

Given equation is:

$\frac{1}{2}{x}^2+\sqrt{11}x+1=0$

By using quadratic formula,

$\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
$\therefore x=\frac{-\sqrt{11}\pm \sqrt{11-\left(4\right)\left(1/2\right)\left(1\right)}}{\left(1\right)}$
$\therefore x=\frac{-\sqrt{11}\pm \sqrt{11-\left(2\right)\left(1\right)\left(1\right)}}{\left(1\right)}$

$x=-\sqrt{11}\pm \sqrt{9}$

$x=-\sqrt{11}\pm 3$

$x=-\sqrt{11}-3,x=-\sqrt{11}+3$

Hence, the given statement is false.