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3 years ago

Find a polynomial f(x) of degree 4 that has the following zeros.

Mathematics

1 answer:

34kurt3 years ago

3 0

Answer:

The answer to your question is (x₁ - 4)(x₂ - 9)(x₃)(x₄ +4)

Step-by-step explanation:

Data

zeros of a polynomial = 4, 9, 0, -1

Process

1.- Equal each root to zero

x₁ = 4 x₂ = 9 x₃ = 0 x₄ = -1

x₁ - 4 = 0 x₂ - 9 = 0 x₃ = 0 x₄ + 1 = 0

2.- Write the terms together

(x₁ - 4)(x₂ - 9)(x₃)(x₄ +4)

3.- Expand to check the answer

(x - 4)(x - 9) = x² -13x + 36

(x² -13x + 36)(x) = x³ - 13x² + 36x

(x³ - 13x² + 36x)(x + 4) = x⁴ - 13x³ + 36x² + 4x³ - 52x² + 144x

= x⁴ - 9x³ - 16x² + 144

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The most appropriate choice for similarity of triangles will be given by -

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What are similar triangles?

Two triangles are said to be similar, if the corrosponding angles of the triangles are same and the corrosponding sides of the triangles are in the same ratio.

Here,

The diagram has been attached here

Let the distance of woman from the pole be x ft and the distance of tip of the shadow to the pole be y ft.

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The two triangles are similar [As height of woman is parallel to the height of pole]

$\frac{y - x}{6}=\frac{y}{18}\\18y - 18x = 6y\\18y - 6y = 18x\\12y = 18x\\y = \frac{18}{12}x\\y = \frac{3}{2}x\\$

To find the speed, we have to differentiate both sides with respect to time 't'

$\frac{dy}{dt} =\frac{3}{2}\frac{dx}{dt}\\\frac{dy}{dt}=\frac{3}{2} \times 4\\\frac{dy}{dt} = 6$

Speed of tip of her shadow = 6 ft

To learn more about similarity of triangles, refer to the link-

brainly.com/question/14285697

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