The sum of all the real values of x satisfyin | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given the equation $2^{(x - 1)(x^2 + 5x - 50)} = 1$.Since $2^0 = 1$,the exponent must be equal to $0$.Therefore,$(x - 1)(x^2 + 5x - 50) = 0$.Facto

Vedclass · Accepted Answer

$-4$

Vedclass · Answer

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

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

Similar Questions

The condition that one root of the equation $ax^2 + bx + c = 0$ is three times the other is

How many roots does the equation $x - \frac{2}{x - 1} = 1 - \frac{2}{x - 1}$ have?

The number of real roots of the equation $e^{4x} + e^{3x} - 4e^{2x} + e^x + 1 = 0$ is:

Sum of the solutions of the equation $[x^2] - 2x + 1 = 0$ is (where $[.]$ denotes the greatest integer function).

Solve the given two equations and select the correct answer from the given options.
$I.$ $7x^2 + 16x - 15 = 0$
$II.$ $y^2 - 6y - 7 = 0$

Vedclass Test Series

Exam Paper Generator

Online Exam Module