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Mathematics
Problem
The quadratic expression
2
x
2
−
8
x
+
3
2x^{2}-8x+3
2
x
2
−
8
x
+
3
is written as
2
(
x
−
α
)
(
x
−
β
)
2(x-\alpha)(x-\beta)
2
(
x
−
α
)
(
x
−
β
)
, where
α
\alpha
α
and
β
\beta
β
are real numbers. Which ordered pair
(
α
,
β
)
(\alpha,\beta)
(
α
,
β
)
is correct? a)
(
2
+
10
,
2
−
10
)
\left(2+\sqrt{10},\,2-\sqrt{10}\right)
(
2
+
10
,
2
−
10
)
b)
(
−
2
+
10
2
,
−
2
−
10
2
)
\left(-2+\dfrac{\sqrt{10}}{2},\,-2-\dfrac{\sqrt{10}}{2}\right)
(
−
2
+
2
10
,
−
2
−
2
10
)
c)
(
2
+
10
2
,
2
−
10
2
)
\left(2+\dfrac{\sqrt{10}}{2},\,2-\dfrac{\sqrt{10}}{2}\right)
(
2
+
2
10
,
2
−
2
10
)
d)
(
2
+
5
2
,
2
−
5
2
)
\left(2+\dfrac{\sqrt{5}}{2},\,2-\dfrac{\sqrt{5}}{2}\right)
(
2
+
2
5
,
2
−
2
5
)
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