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Tems11 [23]
3 years ago
8

Find all the zeroes of the polynomial function f(x)=x^3-5x^2+6x-30 using synthetic division.

Mathematics
1 answer:
WITCHER [35]3 years ago
3 0
Write the coeeficientes of the polynomial in order:

  | 1   - 5   6   - 30
  |
  |
  |
------------------------

After some trials you probe with 5

   | 1   - 5       6     - 30
   |
   |
5 |        5      0       30
-----------------------------
     1     0      6        0 <---- residue

Given that the residue is 0, 5 is a root.

The quotient is x^2 + 6 = 0, which does not have a real root.

Therefore, 5 is the only root. You can prove it by solving the polynomial x^2 + 6 = 0.
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Based on the calculations, the area of the shaded region is equal to 22 square foot.

<h3>How to calculate the area of the shaded region?</h3>

By critically observing the geometric shapes, the area of the shaded region can be calculated by using this formula:

Area of shaded region = Area of square - Area of circle.

<u>Note:</u> The diameter of this circle is equal to the side length of the square because the circumference of this circle lies on the circumference of the square.

Radius = diameter/2 = 10/2 = 5 feet.

For the area of square, we have:

Area of square = S²

Area of square = 10²

Area of square = 100 square foot.

For the area of circle, we have:

Area of circle = πr²

Area of circle = 3.14 × 5²

Area of circle = 78.5 square foot.

Substituting the parameters into the formula, we have;

Area of shaded region = Area of square - Area of circle.

Area of shaded region = 100 - 78.5

Area of shaded region = 21.5 ≈ 22

Area of shaded region = 22 square foot.

Read more on area of circle here: brainly.com/question/2278809

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<h3>Complete Question:</h3>

Find the area to the nearest square foot of the shaded region below, consisting of a square with a circle cut out of it. Use 3.14 as an approximation for π.

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Step-by-step explanation:

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