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Answer :
Final answer:
The zeros of the function c(x) = 3x⁴ - 10x³ - 45x² - 20x + 12 are x = -2, -1, 1/3, and 6.
Explanation:
To find the zeros of the function c(x) = 3x⁴ - 10x³ - 45x² - 20x + 12, we need to solve the equation for when it is equal to zero.
In other words, we set c(x) equal to zero and find the values of x for which this is true. Giving us the equation:
3x⁴ - 10x³ - 45x² - 20x + 12 = 0
We use the rational root theorem to find potential rational zeros of this polynomial, which are p/q such that p is a factor of the constant term (12 in our case) and q is a factor of the leading coefficient (3 in our case). Trying these out, we find that the equation does indeed equal zero for x = -2, -1, 1/3, and 6.
Therefore, the zeros of the function c(x) = 3x⁴ - 10x³ - 45x² - 20x + 12 are x = -2, -1, 1/3, and 6.
Learn more about Zeros of a Polynomial here:
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