(C) Given the equation $2^{(x - 1)(x^2 + 5x - 50)} = 1$. Since $2^0 = 1$,we equate the exponent to $0$: $(x - 1)(x^2 + 5x - 50) = 0$. Factoring the qu

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(C) Given the equation $2^{(x - 1)(x^2 + 5x - 50)} = 1$. Since $2^0 = 1$,we equate the exponent to $0$: $(x - 1)(x^2 + 5x - 50) = 0$. Factoring the quadratic expression $x^2 + 5x - 50$: $(x^2 + 10x - 5x - 50) = x(x + 10) - 5(x + 10) = (x - 5)(x + 10)$. So,the equation becomes $(x - 1)(x - 5)(x + 10) = 0$. The real values of $x$ are $x = 1, 5, -10$. The sum of these values is $1 + 5 + (-10) = 6 - 10 = -4$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

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The sum of all the real values of $x$ satisfying the equation $2^{(x - 1)(x^2 + 5x - 50)} = 1$ is

JEE MAIN 2017 All JEE MAIN

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

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