what is the sign of $-\\frac{a^{4}}{3}$ when $a < 0$?\nchoose 1 answer:\npositive\nnegative\nzero
what is the sign of $-\\frac{a^{4}}{3}$ when $a < 0$?\nchoose 1 answer:\npositive\nnegative\nzero
Answer
Explanation:
Step1: Analyze the sign of (a^4)
When (a\neq0), for any real number (a), (a^4=(a^2)^2). Since (a^2\geq0) for all real (a), and when (a\neq0), (a^2>0). Then ((a^2)^2>0). Given (a < 0) (and (a\neq0)), (a^4>0).
Step2: Analyze the sign of (-\frac{a^4}{3})
We know that (a^4>0), then (\frac{a^4}{3}>0) (because dividing a positive number (a^4) by a positive number (3) results in a positive number). Multiply (\frac{a^4}{3}) by (- 1), we get (-\frac{a^4}{3}<0) (using the rule that (-x) is negative when (x>0)).
Answer:
B. Negative