Question

The number of real solutions of \[\left| 2x - x^2 - 3 \right| = 1\] is

पर्याय

• 0

• 2

• 3

• 4

Answer 1

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.