Question

In the following, determine whether the given quadratic equations have real roots and if so, find the roots :
$x^2$ + x + 2 = 0

• A. $real,-1,0$
• B. $real,-1,1$
• C. $real,1,0$
• D. $\text{not real}$

Answer 1

Answer: (D)

$\text{not real}$

$x^2+x+2=0$

$\Rightarrow$ $a=1,b=1,c=2$

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

$=\frac{-1\pm \sqrt{1^2-4\left(1\right)\left(2\right)}}{2\left(1\right)}$

$=\frac{-1\pm \sqrt{1-8}}{2}$

$=\frac{-1\pm \sqrt{-7}}{2}$

$x=\frac{-1+\sqrt{-7}}{2}$ $x=\frac{-1-\sqrt{-7}}{2}$

$\Rightarrow$ Here we can see roots are not real.