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Problem
Problem
The roots of the equation
−
2
x
2
+
5
x
+
1
=
0
-2x^2 + 5x + 1 = 0
−
2
x
2
+
5
x
+
1
=
0
are
α
\alpha
α
and
β
\beta
β
. a. Find a quadratic equation with roots
α
+
2
\alpha + 2
α
+
2
and
β
+
2
\beta + 2
β
+
2
. b. Find *all* quadratic equations with roots
α
2
\frac{\alpha}{2}
2
α
and
β
2
\frac{\beta}{2}
2
β
.
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