With a quadratic equation that can be factorised is it true to say that a times b = c? Is it really that simpl

Question

With a quadratic equation that can be factorised is it true to say that a times b = c? Is it really that simple?

Answer 1

I don't know.

Let's find out.

How about we start with a factorised equation already and then put it into the form aX^2 + bX + c = 0

let's start with
0 = l.(x + m) (x + n) where l, m and n are just some variables

= l. (x^2 + (m+n)x + mn)

= lX^2 + l(m+n)x + lmn

which is of the form aX^2 + bX + c

does c = a x b?

l x l(m+n) = l^2m + l^2n

I think you are going to find that this does not = lmn all the time

Perhaps you could take it further and discover for what values of l, m and n the equation IS true?

lmn = l^2m + l^2n

when l or (m+n) = 0, for instance...
and any other times?

Answer 2

Absolutely not. For instance, take the quadratic equation x²-2x+1=0. In this case, a=1, b=-2, and c=1. a*b≠c, but this equation trivially factors into (x-1)(x-1).

Answer 3

Yes

Answer 4

ab = c is only true for specialized (custom) quadratics. However, it is not true for every factorizable quadratic.

E.g.
2x² + 5x + 3 = 0
can be factorized as
(2x + 3)(x + 1) = 0

but
ab = 2(5) = 10
c = 3

Therefore, ab is not equal to c.

^_^

Answer 5

Possibly with the odd equation it might work, but not every time.

Answer 6

yes