Multiple choice

State true or false: The roots of the equation $ 24 = x^3 + x^2 + 12$ are $2$ and $ 1$.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Test roots: If x=2, 2^3 + 2^2 + 12 = 8 + 4 + 12 = 24. Correct. If x=1, 1^3 + 1^2 + 12 = 1 + 1 + 12 = 14, not 24. So the statement is false.

AI explanation

Rearranging the equation x^3 + x^2 + 12 = 24 yields x^3 + x^2 - 12 = 0. Checking the proposed root x = 1 gives 1^3 + 1^2 - 12 = -10, which is not zero. Checking the proposed root x = 2 gives 2^3 + 2^2 - 12 = 0, meaning only 2 is a valid root while 1 is not. Therefore, the statement that both 2 and 1 are roots of the equation is false.

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