Sum of the roots of the equation $(x+3)^2-4|x+3|+3=0$ is-
- $4$
- $12$
- $-12$
- $-4$
Reveal answer
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C
Correct answer
Explanation
Let y = |x+3|. The equation is y^2 - 4y + 3 = 0. (y-3)(y-1) = 0. So |x+3| = 3 or |x+3| = 1. Case 1: x+3 = 3 or -3, so x = 0 or -6. Case 2: x+3 = 1 or -1, so x = -2 or -4. Sum = 0 - 6 - 2 - 4 = -12.
AI explanation
Substitute y equals the absolute value of (x plus 3), rewriting the equation as y squared minus 4y plus 3 equals zero. This factors into (y minus 1) times (y minus 3) equals zero, giving values of y as 1 and 3. Since y equals the absolute value of (x plus 3), solving gives the roots for x as negative 2, negative 4, negative 6, and 0, and their sum is negative 12.