Determine Whether x² + x + 2 = 0 Has Real Roots and Find the Roots
Question
Determine whether the given quadratic equation has real roots and if so, find the roots:
\[ x^2+x+2=0 \]Solution
\[ a=1,\quad b=1,\quad c=2 \]
Find the discriminant:
\[ D=b^2-4ac \]
\[ D=(1)^2-4(1)(2) \]
\[ D=1-8 \]
\[ D=-7 \]
Since
\[ D<0 \]
the quadratic equation has no real roots.
Answer
\[
\boxed{\text{The equation } x^2+x+2=0 \text{ has no real roots.}}
\]