Why is delta b^2-4ac where does it come from?

[proven vigil]

for ax^2 + bx + c = 0, you can directly solve for x by completing the square

once you do that, the b^2 - 4ac term is what appears in the square root

then how that b^2 - 4ac term behaves determines how the roots are like:

,,x=-\frac{b}{2a}\pm\frac{\sqrt{b^2-4ac}}{2a}

[livid carbon]

mtt07734

[proven vigil]

theres three possibilities for b^2 - 4ac

if b^2 - 4ac is positive, then youre doing -b/(2a) ± (a positive number) which will get you two different numbers for x
if b^2 - 4ac is 0, then you end up with -b/(2a), which is one number for x
if b^2 - 4ac is negative, then youre square rooting a negative, so you get two different complex numbers for x

so from this,
b^2 - 4ac > 0 means 2 real roots
b^2 - 4ac = 0 means 1 real root (repeated root)
b^2 - 4ac < 0 means 2 complex roots (conjugates)

since the b^2 - 4ac itself can tell you about the roots, it has that special name called the "discriminant" and written with that capital Delta symbol

@blissful cloud does this answer your question

thats what I said

[proven vigil]

read this closer

also dont call it delta, its called the discriminant

[proven vigil]

delta is a greek letter and can be used in other ways like making the 'd' sound

anything else?

alr

.solved