x^2-6x+10 is to be written in the form (x-p)^2 +q Find the values of p and q
Answers
Answered by
1
Answer:
ends up in a form like
x
2
+
a
x
+
b
=
(
x
+
c
)
2
+
d
c
is always half of
a
, so that when you expand out the brackets you have the right coefficients for
x
2
and
x
.
a
=
6
→
c
=
3
(
x
+
3
)
2
=
x
2
+
6
x
+
9
As you can see this is pretty close to the original quadratic. All you need to do is add
1
and it equates perfectly.
x
2
+
6
x
+
10
=
(
x
+
3
)
2
+
1
To then solve, rearrange like so
(
x
+
3
)
2
+
1
=
0
(
x
+
3
)
2
=
−
1
x
+
3
=
√
−
1
=
±
i
x
=
±
i
−
3
Similar questions