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

The Correct Option is C

\(|x^{2}-8x+15|=2x-7\)

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 + \(\sqrt{3}\)