what is the factor of x²-3x-1
Answers
Answered by
2
Answer:
It requires irrational coefficients, but...
Complete the square and use the difference of squares identity to find:
y
=
x
2
−
3
x
−
1
=
(
x
−
3
2
−
√
13
2
)
(
x
−
3
2
+
√
13
2
)
Explanation:
Note that:
(
x
−
3
2
)
2
=
x
2
−
3
x
+
9
4
Also, the difference of squares identity can be written:
a
2
−
b
2
=
(
a
−
b
)
(
a
+
b
)
We use this with
a
=
(
x
−
3
2
)
and
b
=
√
13
2
below...
y
=
x
2
−
3
x
−
1
=
x
2
−
3
x
+
9
4
−
9
4
−
1
=
(
x
−
3
2
)
2
−
13
4
=
(
x
−
3
2
)
2
−
(
√
13
2
)
2
=
(
(
x
−
3
2
)
−
√
13
2
)
(
(
x
−
3
2
)
+
√
13
2
)
=
(
x
−
3
2
−
√
13
2
)
(
x
−
3
2
+
√
13
2
)
Answered by
0
Answer:
product is equal to X
sum is equal to 3 x
x square - 2x plus x - 1
2x(x-1)(x-1)
(2x+1)(x-1)
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