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Question
The number of real solutions of \[\left| 2x - x^2 - 3 \right| = 1\] is
Options
0
2
3
4
Solution
2
Explanation:
Given equation:
\[|2x - x^2 - 3| = 1\]
\[ 2x - x^2 - 3 = 1\]
\[ \Rightarrow 2x - x^2 - 4 = 0\]
\[ \Rightarrow x^2 - 2x + 4 = 0\]
Discriminant D = 4 - 16
= -12 < 0
Hence the roots are unreal.
\[- 2x + x^2 + 3 = 1\]
= x2 – 2x -2 = 0
Discriminant, D = 4 – 8 = - 4 < 0
Hence the given equation has no real roots.
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