Question

If f $(5+x) = f (5-x)$ for every real x, and $f(x)=0$ has four distinct real roots, then the sum of these roots is

• A. 0
• B. 40
• C. 10
• D. 20

Answer 1

Answer: (D)

20

Answer 2

The correct answer is (D): $20$

Given $f (5+x) = f (5-x)$

Put $x = x-5$

$f(x) = f(10-x)$

Let a, b be two roots of $f(x)=0$, then $10-a,10-b$ are also roots of $f (x) = 0$

$∴$ Hence sum of the roots = $a+b+10-a+10-b=20$