The sum of all the real values of x satisfying the equation 2(x$$-$$1)(x2 + 5x $$-$$ 50) = 1 is :
JEE · Math · previous-year question
- A.16
- B.14
- C.$$-$$4correct
- D.$$-$$ 5
Answer
C. $$-$$4
Explanation
We know, 2x = 1 only when x = 0. Similarly, 2(x$$-$$1)(x2 + 5x $$-$$ 50) = 1 when (x$$-$$1)(x2 + 5x $$-$$ 50) = 0 $$ \Rightarrow $$ (x - 1)(x + 10)(x - 5) = 0 $$ \therefore $$ x = 1, -10, 5 Sum of real values of x = 1 + (-10) + 5 = -4
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