Multiple choice

If $f(x)$ is a quadratic expression such that $f(1) + f(2) = 0$, and $-1$ is a root of $f(x) = 0$, then the other root of $f(x) = 0$ is :

  1. $-\dfrac {5}{8}$
  2. $-\dfrac {8}{5}$
  3. $\dfrac {5}{8}$
  4. $\dfrac {8}{5}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let f(x) = a(x+1)(x-r). f(1) = 2a(1-r) and f(2) = 3a(2-r). f(1)+f(2) = 0 implies 2a(1-r) + 3a(2-r) = 0. Dividing by a (assuming a is not 0), 2 - 2r + 6 - 3r = 0, so 8 - 5r = 0, r = 8/5.

AI explanation

Let f(x) = a(x + 1)(x - r), where -1 and r are the roots. We calculate f(1) = a(2)(1 - r) and f(2) = a(3)(2 - r). Since f(1) + f(2) = 0, we have 2a(1 - r) + 3a(2 - r) = 0, which simplifies to 8 - 5r = 0. Solving this yields r = 8/5.

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