# 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. Philomena
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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