Find the discriminent of 2x²-5x+5=0
Answers
Answer:
this quadratic,
Δ
=
−
15
, which means that the equation has no real solutions, but it does have two distinct complex ones.
Explanation:
The general form for a quadratic equation is
a
x
2
+
b
x
+
c
=
0
The general form of the discriminant looks like this
Δ
=
b
2
−
4
⋅
a
⋅
c
Your equation looks like this
2
x
2
+
5
x
+
5
=
0
which means that you have
⎧
⎪
⎨
⎪
⎩
a
=
2
b
=
5
c
=
5
The discriminant will thus be equal to
Δ
=
5
2
−
4
⋅
2
⋅
5
Δ
=
25
−
40
=
−
15
The two solutions for a general quadratic are
x
1
,
2
=
−
b
±
√
Δ
2
a
When
Δ
<
0
, such as you have here, the equation is said to have no real solutions, since you're extracting the square root from a negative number.
However, it does have two distinct complex solutions that have the general form
x
1
,
2
=
−
b
±
i
√
−
Δ
2
a
, when
Δ
<
0
In your case, these solutions are
x
1
,
2
=
−
5
±
√
−
15
4
=
⎧
⎪
⎨
⎪
⎩
x
1
=
−
5
+
i
√
15
4
x
2
=
−
5
−
i
√
15
4