Write the Discriminant of the Quadratic Equation (x − 1)(2x − 1) = 0
Question
Write the discriminant of the following quadratic equation:
\[ (x-1)(2x-1)=0 \]Solution
First, expand the equation:
\[ 2x^2-3x+1=0 \]
\[ a=2,\quad b=-3,\quad c=1 \]
Using the formula,
\[ D=b^2-4ac \]
Substituting the values,
\[ D=(-3)^2-4(2)(1) \]
\[ D=9-8 \]
\[ D=1 \]
Answer
\[
\boxed{D=1}
\]