JEE MainMathematicsQuadratic Equation

The product of all real roots of the equation (x-1)²-3|x-1|-10=0 is :

Options

A-24
B72
C-6
D-10

Correct answer

A. -24

Step-by-step solution

Let t = |x-1| , where t 0 . The given equation becomes: t^2 - 3t - 10 = 0 (t-5)(t+2) = 0 t = 5 or t = -2 Since t = |x-1| cannot be negative, we reject t = -2 . For t = 5 : |x-1| = 5 x - 1 = 5 or x - 1 = -5 x = 6 or x = -4 The real roots of the equation are 6 and -4 . The product of all real roots is 6 (-4) = -24 . Answer: -24

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