Beginner here. Can I ask someone to explain to me the following?
Given the following general form of quadratic equation:
$$
ax^2+bx+c=0
$$
and the following formula for discriminant:
$$
D=b^2−4ac,
$$
what is the $b$ coefficient in the following equation?
$$
2x^2 – 2x = 0
$$
Is it $-2$ or $2$?
Does the coefficient count with the positive/negative sign?
I am confused because for example $-2^2= -4$, and so here the sign is not taken into consideration, unless it's $(-2)^2$.
Best Answer
Considering the general form $$ ax^2+bx+c=0 $$ $$\implies b=-2$$ Since $$x^2-2x=x^2+(-2)x$$ The discriminant would be the same even if $b=2$, but $x$ will be affected, this is because if we look at the $-b$ term: $$ x = \cfrac{-b\pm\sqrt{b^2-4ac}}{2a} $$ $$ -(-2)=2\neq -2 $$