Write the Discriminant of the Quadratic Equation (x + 5)² = 2(5x − 3)
Question
Write the discriminant of the following quadratic equation:
\[ (x+5)^2=2(5x-3) \]Solution
First, simplify the equation:
\[ x^2+10x+25=10x-6 \]
\[ x^2+31=0 \]
\[ a=1,\quad b=0,\quad c=31 \]
Using the formula,
\[ D=b^2-4ac \]
Substituting the values,
\[ D=(0)^2-4(1)(31) \]
\[ D=-124 \]
Answer
\[
\boxed{D=-124}
\]