JEE Main202124 Feb 2021Evening ShiftMathematicsQuadratic EquationActual

The number of the real roots of the equation x + 1 2 + | x - 5 | = 27 4 is ________.

Correct answer

Step-by-step solution

Case- I x ≤ 5 x + 1 2 - x - 5 = 27 4 x + 1 2 - x + 1 - 3 4 = 0 x + 1 = 3 2 , - 1 2 x = 1 2 , - 3 2 Case- II x > 5 x + 1 + x - 5 = 27 4 x + 1 2 + x + 1 - 51 4 = 0 x = - 1 ± 52 2 (rejected as x > 5 ) So, the equation have two real root.

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