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Answer :
Final answer:
The polynomial function with the lowest degree and a leading coefficient of 1, with roots √3, -4, and 4, is f(x) = (x² - 3)(x + 4)(x - 4).
Explanation:
To find the polynomial function with the lowest degree and a leading coefficient of 1, we can use the fact that the roots are √3, -4, and 4. Since square roots are involved, the degree of the polynomial will be at least 2. We know that the factors of the polynomial will be (x - √3), (x + 4), and (x - 4) because those are the values that make the polynomial equal to 0 at its roots. Multiplying these factors together gives us the polynomial function of lowest degree:
f(x) = (x - √3)(x + 4)(x - 4)
Simplifying further, we get:
f(x) = (x² - 3)(x + 4)(x - 4)
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