Question

The sum of all real roots of the equation $x^2+15=8|x|$ is

• A. $0$
• B. $6$
• C. $10$
• D. $16$

Answer 1

The correct option is A $0$

Consider given the equation,

$x^2+15=8\left|x\right|$

$ifx\ge 0$

Then equation become,

$x^2+15=8x$

$x^2-8x+15=0$

$x^2-5x-3x+15=0$

$x(x-5)-3(x-5)=0$

$(x-5)(x-3)=0$

$x=5orx=3$

If $x<0$

Then equation become,

$x^2+15=-8x$

$x^2+15=-8x$

$x^2+8x+15=0$

$(x+5)(x+3)=0$

$x=-5orx=-3$

Hence, there are real roots are $5$ and $3$

Sum of real roots are$5+3-5-3=0$

Hence, this is the answer.