Determine Whether 3x² − 2x + 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:
\[ 3x^2-2x+2=0 \]Solution
\[ a=3,\quad b=-2,\quad c=2 \]
Find the discriminant:
\[ D=b^2-4ac \]
\[ D=(-2)^2-4(3)(2) \]
\[ D=4-24 \]
\[ D=-20 \]
Since
\[ D<0 \]
the quadratic equation has no real roots.
Answer
\[
\boxed{\text{The equation } 3x^2-2x+2=0 \text{ has no real roots.}}
\]