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Mathematics
Mathematics
Problem
Let
α
,
β
\alpha, \beta
α
,
β
be the roots of the quadratic equation
a
x
2
+
b
x
+
c
=
0
ax^2 + bx + c = 0
a
x
2
+
b
x
+
c
=
0
, then the roots of the equation
a
(
x
+
1
)
2
+
b
(
x
+
1
)
(
x
−
2
)
+
c
(
x
−
2
)
2
=
0
a(x+1)^2 + b(x+1)(x-2) + c(x-2)^2 = 0
a
(
x
+
1
)
2
+
b
(
x
+
1
)
(
x
−
2
)
+
c
(
x
−
2
)
2
=
0
are : (a)
2
α
+
1
α
−
1
,
2
β
+
1
β
−
1
\frac{2\alpha+1}{\alpha-1}, \frac{2\beta+1}{\beta-1}
α
−
1
2
α
+
1
,
β
−
1
2
β
+
1
(b)
2
α
−
1
α
+
1
,
2
β
−
1
β
+
1
\frac{2\alpha-1}{\alpha+1}, \frac{2\beta-1}{\beta+1}
α
+
1
2
α
−
1
,
β
+
1
2
β
−
1
(c)
α
+
1
α
−
2
,
β
+
1
β
−
2
\frac{\alpha+1}{\alpha-2}, \frac{\beta+1}{\beta-2}
α
−
2
α
+
1
,
β
−
2
β
+
1
(d)
2
α
+
3
α
−
1
,
2
β
+
3
β
−
1
\frac{2\alpha+3}{\alpha-1}, \frac{2\beta+3}{\beta-1}
α
−
1
2
α
+
3
,
β
−
1
2
β
+
3
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