find the discriminant of the quadratic equation x²-x+1=0
Answers
Answer:
Step-by-step explanation:
The given equation is in the form of ax²+bx+c=0
here a = 1, b = -1 and c=1
The discriminant is D=b²-4ac
⇒(−1)² −4×1×1
⇒1-4 =-3
Therefore The discriminant D, of the following quadratic equation is -3
Answer:
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What is the discriminant of
x
2
+
x
+
1
=
0
and what does that mean?
Algebra Solutions Using the Discriminant
1 Answer
Ernest Z.
Jul 16, 2015
The discriminant is -3. It tells you that there are no real roots, but there are two complex roots to the equation.
Explanation:
If you have a quadratic equation of the form
a
x
2
+
b
x
+
c
=
0
The solution is
x
=
−
b
±
√
b
2
−
4
a
c
2
a
The discriminant
Δ
is
b
2
−
4
a
c
.
The discriminant "discriminates" the nature of the roots.
There are three possibilities.
If
Δ
>
0
, there are two separate real roots.
If
Δ
=
0
, there are two identical real roots.
If
Δ
<
0
, there are no real roots, but there are two complex roots.
Your equation is
x
2
+
x
+
1
=
0
Δ
=
b
2
–
4
a
c
=
1
2
−
4
×
1
×
1
=
1
–
4
=
−
3
This tells you that there are no real roots, but there are two complex roots.
We can see this if we solve the equation.
x
2
+
x
+
1
=
0
x
=
−
b
±
√
b
2
−
4
a
c
2
a
=
−
1
±
√
1
2
−
4
×
1
×
1
2
×
1
=
−
1
±
√
1
−
4
2
=
−
1
±
√
−
3
2
=
1
2
(
−
1
±
i
√
3
)
=
−
1
2
(
1
±
i
√
3
)
x
=
—
1
2
(
1
+
i
√
3
)
and
x
=
−
1
2
(
1
−
i
√
3
)