find the zeros of x square - 12x+ 32
Answers
Answered by
0
x^2 - 12x + 32 = 0
So,
x^2 - 8x - 4x + 32 = 0
(x-8)(x-4) = 0
Therefore,
x-8=0 and x-4=0
So,
x = 4 and x = 8 are the two zeroes of the given quadratic equation.
So,
x^2 - 8x - 4x + 32 = 0
(x-8)(x-4) = 0
Therefore,
x-8=0 and x-4=0
So,
x = 4 and x = 8 are the two zeroes of the given quadratic equation.
Answered by
0
Answer:
x
=
4
or
x
=
8
Explanation:
Method 1 - Finding a pair of factors
Find a pair of factors of
32
with sum
12
.
The pair
4
,
8
works in that
4
×
8
=
32
and
4
+
8
=
12
Hence we find:
0
=
x
2
−
12
x
+
32
=
(
x
−
4
)
(
x
−
8
)
So
x
=
4
or
x
=
8
Method 2 - Completing the square
0
=
x
2
−
12
x
+
32
=
x
2
−
2
(
6
x
)
+
36
−
4
=
(
x
−
6
)
2
−
2
2
=
(
(
x
−
6
)
−
2
)
(
(
x
−
6
)
+
2
)
=
(
x
−
8
)
(
x
−
4
)
Hence
x
=
8
or
x
=
4
Method 3 - Quadratic formula
x
2
−
12
x
+
32
=
0
is in the form
a
x
2
+
b
x
+
c
=
0
with
a
=
1
,
b
=
−
12
,
c
=
32
This has roots given by the quadratic formula:
x
=
−
b
±
√
b
2
−
4
a
c
2
a
=
12
±
√
12
2
−
4
(
1
)
(
32
)
2
⋅
1
=
12
±
√
144
−
128
2
=
12
±
√
16
2
=
12
±
4
2
=
6
±
2
So
x
=
8
or
x
=
4
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