The sum of all the roots of the equation ∣∣x2−8x+15∣∣−2x+7=0 is

To solve this problem, we first need to find the roots of the equation inside the absolute value bars, which is a quadratic equation.

The quadratic equation is x^2 - 8x + 15 = 0.

We can solve this equation by factoring, completing the square, or using the quadratic formula. In this case, factoring is the easiest method.

We look for two numbers that multiply to 15 and add to -8. The numbers -3 and -5 meet these criteria.

So, we can factor the equation as (x - 3)(x - 5) = 0.

Setting each factor equal to zero gives us the roots x = 3 and x = 5.

However, because the original equation involves absolute values, we also need to consider the possibility of negative roots.

When we substitute x = 3 and x = 5 into the absolute value equation, we find that both roots satisfy the equation.

Therefore, the roots of the original equation are 3, 5, -3, and -5.

The sum of these roots is 3 + 5 - 3 - 5 = 0.