Question

The sum of roots of |x2 - 8x + 15| - 2x + 7 = 0 is:

• A. $11+\sqrt{3}$
• B. $11-\sqrt{3}$
• C. $9+\sqrt{3}$
• D. $9-\sqrt{3}$

Answer 1

Answer: (C)

$9+\sqrt{3}$

Answer 2

$|x^{2}-8x+15|=2x-7$

Case-I : $x\geq 5$

$x^{2}-10x+22=0$

$x=\frac{10\pm \sqrt{12}}{2}=5\pm \sqrt{3}$

then $x= 5+\sqrt{3}$

Case-II : $\frac{7}{2}\leq x\leq 5$

$x^{2}-8x+15=7-2x$

$x^{2}-6x+8=0$

$x=4$

Therefore, the sum of the roots $= 5+\sqrt{3}+4=9+\sqrt{3}$
So, The correct option is (C): 9 + $\sqrt{3}$