Multiple choice

If one root of the equation $\displaystyle { x }^{ 2 }+7x+a=0$ is $-2$, then find the value of $a$.

  1. $-9$
  2. $10$
  3. $-10$
  4. $9$
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B Correct answer
Explanation

If -2 is a root, then (-2)^2 + 7(-2) + a = 0. 4 - 14 + a = 0, so a = 10.

AI explanation

If negative 2 is a root of the equation x squared plus 7x plus a equals 0, it must satisfy the equation. Substituting negative 2 for x gives negative 2 squared plus 7 times negative 2 plus a equals 0, which simplifies to 4 minus 14 plus a equals 0. Solving this yields a minus 10 equals 0, so a equals 10.

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