Nature of roots x^2+5x+6=0
Answers
Answered by
0
Answer:
the nature of the roots are positive
Answered by
1
Step-by-step explanation:
In a quadratic in the form
a
x
2
+
b
x
+
c
, find two numbers that multiply to
a
⋅
c
and add up to
b
in order to factor.
In this case, we need two numbers that multiply to
6
and add up to
−
5
. These two numbers are
−
2
and
−
3
.
Now, split up the
x
term into these two numbers. Next, factor the first two terms and the last two terms separately, then combine them. Lastly, set each factor equal to zero and solve for
x
in each one. Here's what all that looks like:
x
2
−
5
x
+
6
=
0
x
2
−
2
x
−
3
x
+
6
=
0
x
(
x
−
2
)
−
3
x
+
6
=
0
x
(
x
−
2
)
−
3
(
x
−
2
)
=
0
(
x
−
3
)
(
x
−
2
)
=
0
x
−
3
=
0
x
−
2
=
0
x
=
3
x
=
2
These are the two solutions. Hope this helped!
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