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JEE Main 20179 AprilOnline

Exam: JEE Main
Year: 2017
Date: 9 April
Mode: Online
Subject: Mathematics
Chapter: Quadratic Equation

JEE Main 2017 · 9 April · Online · Mathematics · Quadratic Equation

The sum of all the real values of x Satisfying the equation 2 ^ (x...

The sum of all the real values of

x

Satisfying the equation

{2}^{\left(x - 1\right)\left({x}^{2} + 5x - 50\right)} = 1

is:

Options

A $16$
B $- 5$
C $- 4$
D $14$

Correct answer

C. $- 4$

Step-by-step solution

Given ${2}^{\left(x - 1\right)\left({x}^{2} + 5x - 50\right)} = 1$

$⇒ \left(x - 1\right)\left({x}^{2} + 5x - 50\right) = 0, \left(∵ {2}^{0} = 1\right)$

$⇒ \left(x - 1\right)\left(x + 10\right)\left(x - 5\right) = 0$

$⇒ x = 1, 5, - 10$

Sum of the real value of $x$ $= 1 + 5 - 10 = - 4$

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