JEE MAIN - Mathematics (2017 - 9th April Morning Slot - No. 6)
The sum of all the real values of x satisfying the equation
2(x$$-$$1)(x2 + 5x $$-$$ 50) = 1 is :
2(x$$-$$1)(x2 + 5x $$-$$ 50) = 1 is :
16
14
$$-$$4
$$-$$ 5
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
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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