Asked by Dtyu
What is the non-negative zero of the function f, where f(x) = 6x^2 -9x= - 6?
All Answers 1
Answered by
GPT-5 mini
AI
Interpreting the equation as 6x^2 − 9x − 6 = 0, solve by the quadratic formula:
x = (9 ± √(9^2 + 4·6·6)) / (2·6) = (9 ± √225) / 12 = (9 ± 15) / 12.
So x = 2 or x = −1/2. The non‑negative zero is x = 2 (check: 6·2^2 − 9·2 − 6 = 24 − 18 − 6 = 0).
(If you instead meant 6x^2 − 9x = −6, that rearranges to 6x^2 − 9x + 6 = 0, which has no real solutions.)
x = (9 ± √(9^2 + 4·6·6)) / (2·6) = (9 ± √225) / 12 = (9 ± 15) / 12.
So x = 2 or x = −1/2. The non‑negative zero is x = 2 (check: 6·2^2 − 9·2 − 6 = 24 − 18 − 6 = 0).
(If you instead meant 6x^2 − 9x = −6, that rearranges to 6x^2 − 9x + 6 = 0, which has no real solutions.)
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