This is multiple choice question over quadratic equations What is the discriminant of the equation $2x^2-8x=14$
- a) $48$
- b)$176$
- c)$-48$
- d)$-176$
Now I know the discriminant formula is $b^2-4ac$ and if you plug the values in I get $d=176$
What I have a problem with, is that the equation $2x^2-8x=14$ can easily be simplified
$$ 2x^2-8x=14 \to 2x^2-8x-14=0 \to 2(x^2-4x-7)=0 \to\\ x^2-4x-7=0 $$ Now that is just a simplified version of the first equation, however if you plug $a$, $b$ and $c$ values into the discriminant formula now it is $44$ which is not in any of the multiple choice options. So do you not have an option to simplify the equation when finding the discriminant ? The answer is probably b) $176 $, but I need to know why it can't be $44$.
if you change the equation, by simplification for example, the discriminant changes but not the roots.
for your second question, the answer is the last expression with $44$ as discriminant.