Multiple choice

If $x = -4$ is one root of the equation $x^{2} + 2xr + r^{2} = 0$, then the value of $r$ is

  1. $4$
  2. $2$
  3. $-4$
  4. $-2$
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A Correct answer
Explanation

Substitute x = -4 into the equation: (-4)^2 + 2(-4)r + r^2 = 0. 16 - 8r + r^2 = 0. (r-4)^2 = 0. So r = 4.

AI explanation

Substitute x = -4 into the given equation to find r, resulting in (-4)^2 + 2(-4)r + r^2 = 0. This simplifies to 16 - 8r + r^2 = 0, which can be rewritten as (r - 4)^2 = 0 using the perfect square identity. Taking the square root of both sides yields r - 4 = 0, meaning r = 4.

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