Determine Whether x² − 2x + 1 = 0 Has Real Roots and Find the Roots
Question
Determine whether the given quadratic equation has real roots and if so, find the roots:
\[ x^2-2x+1=0 \]Solution
\[ a=1,\quad b=-2,\quad c=1 \]
Find the discriminant:
\[ D=b^2-4ac \]
\[ D=(-2)^2-4(1)(1) \]
\[ D=4-4 \]
\[ D=0 \]
Since
\[ D=0 \]
the equation has two equal real roots.
\[ x=\frac{-b}{2a} \]
\[ x=\frac{2}{2} \]
\[ x=1 \]
Answer
\[
\boxed{x=1}
\]
The equation has two equal real roots.