Question

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

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

Answer 1

Answer: (D)

$-4$

For $2^{(x-1)(x^2+5x-50)}=1$

$(x-1)(x^2+5x-50)=0$

$\therefore x-1=0$ or $x^2+5x-50=0$

If $x-1=0\Rightarrow x=1$

If $x^2+5x-50=0$, then

$x^2+10x-5x-50=0$

$x(x+10)-5(x+10)=0$

$(x+10)(x-5)=0$

$x=-10,5$

Real values of $x=-10,1,5$

sum of the real values of x$=-10+5+1=-4$.