See explanation below.
Explanation:
The 'difference between roots and factors of an equation' is not a straightforward question. Let's define both to establish the link between the two..
Assume we have some function of a single variable
x
;
we'll call this
f
(
x
)
Then we can form an equation:
f
(
x
)
=
0
Then the "roots" of this equation are all the values of
x
that satisfy that equation. Remember that these values may be real and/or imaginary.
Now, up to this point we have not assumed anything about
f
x
)
. To consider factors, we now need to assume that
f
(
x
)
=
g
(
x
)
⋅
h
(
x
)
.
That is that
f
(
x
)
factorises into some functions
g
(
x
)
×
h
(
x
)
If we recall our equation:
f
(
x
)
=
0
Then we can now say that either
g
(
x
)
=
0
or
h
(
x
)
=
0
.. and thus show the link between the roots and factors of an equation.
[NB: A simple example of these general principles would be where
f
(
x
)
is a quadratic function that factorises into two linear factors.
Answer:
<h2>5 + 3w + 3 - w = 2w + 8</h2>
Step-by-step explanation:
Answer:
The proof is derived from the summarily following equations;
∠FBE + ∠EBD = ∠CBA + ∠CBD
∠FBE + ∠EBD = ∠FBD
∠CBA + ∠CBD = ∠ABD
Therefore;
∠ABD ≅ ∠FBD
Step-by-step explanation:
The two column proof is given as follows;
Statement 
Reason
bisects ∠CBE Given
Therefore;
∠EBD ≅ ∠CBD Definition of angle bisector
∠FBE ≅ ∠CBA Vertically opposite angles are congruent
Therefore, we have;
∠FBE + ∠EBD = ∠CBA + ∠CBD Transitive property
∠FBE + ∠EBD = ∠FBD Angle addition postulate
∠CBA + ∠CBD = ∠ABD Angle addition postulate
Therefore;
∠ABD ≅ ∠FBD Transitive property.
