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Rasek [7]
2 years ago
14

Using the graph, determine the coordinates of the roots of the parabola.

Mathematics
1 answer:
Mazyrski [523]2 years ago
8 0

The roots are located at (2,0) and (4,0)

In short, the roots are x = 2 and x = 4

The term "x intercept" is another way of saying "root". Both describe the location where the graph crosses the x axis.

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What are the fourth roots of 6+6√(3i) ?
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Answer:

Step-by-step explanation:

The genral form of a complex number in rectangular plane is expressed as z = x+iy

In polar coordinate, z =rcos ∅+irsin∅ where;

r is the modulus = √x²+y²

∅ is teh argument = arctan y/x

Given thr complex number z = 6+6√(3)i

r = √6²+(6√3)²

r = √36+108

r = √144

r = 12

∅ = arctan 6√3/6

∅ = arctan √3

∅ = 60°

In polar form, z = 12(cos60°+isin60°)

z = 12(cosπ/3+isinπ/3)

To get the fourth root of the equation, we will use the de moivres theorem; zⁿ = rⁿ(cosn∅+isinn∅)

z^1/4  = 12^1/4(cosπ/12+isinπ/12)

When n = 1;

z1 =  12^1/4(cosπ/3+isinn/3)

z1 = 12^1/4cis(π/3)

when n = 2;

z2 = 12^1/4(cos2π/3+isin2π/3)

z2 = 12^1/4cis(2π/3)

when n = 3;

z2 = 12^1/4(cosπ+isinπ)

z2 = 12^1/4cis(π)

when n = 4;

z2 = 12^1/4(cos4π/3+isin4π/3)

z2 = 12^1/4cis(4π/3)

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