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Mathematics
Mathematics
Problem
Let
a
,
b
a, b
a
,
b
and
c
c
c
be distinct non-negative numbers and the vectors
a
i
+
a
j
+
c
k
a\mathbf{i} + a\mathbf{j} + c\mathbf{k}
a
i
+
a
j
+
c
k
,
i
+
k
\mathbf{i} + \mathbf{k}
i
+
k
,
c
i
+
c
j
+
b
k
c\mathbf{i} + c\mathbf{j} + b\mathbf{k}
c
i
+
c
j
+
b
k
lie in a plane, then the quadratic equation
a
x
2
+
2
c
x
+
b
=
0
ax^2 + 2cx + b = 0
a
x
2
+
2
c
x
+
b
=
0
has a. real and equal roots b. real and unequal roots c. unreal roots d. both roots real and positive
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