find the discriminant of the followung equation x2+5x_6=0
Answers
Answer:
1
Step-by-step explanation:
Answer:
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Step-by-step explanation:
The discriminant of a quadratic is the expression inside the radical of the quadratic formula.
For a quadratic equation that has the general form
a
x
2
+
b
x
+
c
=
0
the discriminant can be calculated by the formula
Δ
=
b
2
−
4
⋅
a
⋅
c
Rearrange your quadratic by adding
−
6
to both sides of the equation
x
2
−
5
x
−
6
=
6
−
6
x
2
−
5
x
−
6
=
0
In your case, you have
a
=
1
,
b
=
−
5
, and
c
=
−
6
, so the discriminant will be equal to
Δ
=
(
−
5
)
2
−
4
⋅
1
⋅
(
−
6
)
Δ
=
25
+
24
=
49
SInce
Δ
>
0
, this quadratic equation will have two disctinct real solutions. Moreover, because
Δ
is a perfect square, those two solutions will be rational numbers.
The general form of the two solutions is given by the quadratic formula
x
1
,
2
=
−
b
±
√
Δ
2
a
In your case, these two solutions will be
x
1
,
2
=
−
(
−
5
)
±
√
49
2
⋅
1
=
5
±
7
2
so that
y
=
x
2
−
5
x
−
6
=
0
In this case, (a - b + c = 0), use the shortcut --> 2 real roots--> - 1 and
(
−
c
a
=
6
)
.
REMINDER of SHORCUT
When (a + b + c = 0) --> 2 real roots: 1 and
c
a
When (a - b + c = 0) --> 2 real roots: - 1 and
(
−
c
a
)
Remember this shortcut. It will save you a lot of time and effort.
