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QUADRATIC EQUATIONS - Coggle Diagram
QUADRATIC EQUATIONS
For
a, b, c ∈ R
and
a ≠ 0
, if the expression with three terms
ax²+bx+c
can be factor out in the equation of
ax²+bx+c=0
the solution set is found by following way:
The "
solutions
" to the Quadratic Equation are where it is equal to
zero
. They are also called "
roots
", or sometimes "
zeros
"
There are usually 2 solutions (as shown in this graph).
The imaginary number “
i
” is defined as the number whose square is -1.
The expressions in the form of
ax²+bx+c=0
are called
quadratic
equations
.
a
,
b
and
c
are known values.
a
can't be 0.
"
x
" is the
variable
or
unknown
.
To find the solution we can use the special
Quadratic Formula
The ± means there are
two
answers:
This is called the
discriminant
.
When it is
0
there are
two equal roots
such that
When
b2 − 4ac
is
positive
, there are
two distinct real roots
such that
When it is
negative
there is
no real root
and the solution set is empty on R.
EXAMPLE
: Solve
5x^2 + 2x + 1 = 0
2)
Note that the discriminant is negative:
3)
Use the quadratic formula:
1)
Coefficients are: a=5, b=2, c=1
4)
5)
So:
Answer:
x = −0,2 ± 0,4i
