Determine the total number of roots of each polynomial function. f (x) = 3×6 + 2×5 + x4 – 2×3 6 g(x)

Determine the total number of roots of each polynomial function.

f (x) = 3×6 + 2×5 + x4 – 2×3

6
g(x) = 5x – 12×2 + 3

2
f (x) = (3×4 + 1)2

8
g(x) = (x – 5)2 + 2×3

3

here are the answers hope this helps

2 thoughts on “Determine the total number of roots of each polynomial function. f (x) = 3×6 + 2×5 + x4 – 2×3 6 g(x)”

  1. The total number of roots of each polynomial function as required in the task content are as follows;
    • f (x) = 3x⁶ + 2x⁵ + x⁴ – 2x³ has 6 roots.
    • g(x) = 5x – 12x² + 3 has 2 roots.
    • f(x) = (3x⁴ + 1)² has 8 roots.
    • g(x) = (x – 5)² + 2x³ has 3 roots.

    What are the total number of roots for each of the given functions?

    The degree of a polynomial very much determines the number of roots such polynomial function would have.
    In this light, if the degree of a polynomial function, P(x) is n; it follows that the total number of roots of the function is; n.
    The number of roots of the polynomial function are therefore as follows;
    For f(x) = 3x⁶ + 2x⁵ + x⁴ + 2x³
    Since the degree is 6; Total number of roots = 6.
    For g(x) = 5x – 12x² + 3
    Since the degree is 2 as it is a quadratic function; Total number of roots = 2.
    For f(x) = (3x⁴ + 1)² = 9x⁸ + 6x⁴ + 1
    Since the degree is 8; Total number of roots = 8.
    For g(x) = (x – 5)² + 2x³
    Since the degree is 3; Total number of roots = 3.
    Ultimately, the total number of roots for each of the given functions are as listed above.
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