Write the Discriminant of the Quadratic Equation x² − 2x + k = 0
Question
Write the discriminant of the following quadratic equation:
\[ x^2-2x+k=0,\quad k\in R \]Solution
\[ a=1,\quad b=-2,\quad c=k \]
Using the formula,
\[ D=b^2-4ac \]
Substituting the values,
\[ D=(-2)^2-4(1)(k) \]
\[ D=4-4k \]
\[ D=4(1-k) \]
Answer
\[
\boxed{D=4-4k=4(1-k)}
\]