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3 years ago

A polynomial has a leading coefficient of 1 and the

Mathematics

2 answers:

Hoochie [10]3 years ago

7 0

Answer:

(A) $[x-(2+i)][x-(2-i)][x-\sqrt{2}][x+\sqrt{2}]$

Step-by-step explanation:

A polynomial has a leading coefficient of 1 and the following factors with multiplicity 1:

$x-(2+i)\\x-\sqrt{2}$

We apply the following to find the factored form of the polynomial.

If a complex number is a root of a polynomial with real coefficients, its complex conjugate is also a root of that polynomial.

If the polynomial has an irrational root $a+\sqrt{b}$ , where a and b are rational and b is not a perfect square, then it has also a conjugate root $a-\sqrt{b}$ .

$\text{Complex conjugate of }x-(2+i)=x-(2-i)\\\\\text{Complex conjugate of }x-\sqrt{2}=x+\sqrt{2}$

Therefore, the factored form of the polynomial is:

$[x-(2+i)][x-(2-i)][x-\sqrt{2}][x+\sqrt{2}]$

Nutka1998 [239]3 years ago

7 0

Answer:C

Step-by-step explanation:

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For all values of x

Yuliya22 [10]

Answer:

A.) gf(x) = 3x^2 + 12x + 9

B.) g'(x) = 2

Step-by-step explanation:

A.) The two given functions are:

f(x) = (x + 2)^2 and g(x) = 3(x - 1)

Open the bracket of the two functions

f(x) = (x + 2)^2

f(x) = x^2 + 2x + 2x + 4

f(x) = x^2 + 4x + 4

and

g(x) = 3(x - 1)

g(x) = 3x - 3

To find gf(x), substitute f(x) for x in g(x)

gf(x) = 3( x^2 + 4x + 4 ) - 3

gf(x) = 3x^2 + 12x + 12 - 3

gf(x) = 3x^2 + 12x + 9

Where

a = 3, b = 12, c = 9

B.) To find g '(12), you must first find the inverse function of g(x) that is g'(x)

To find g'(x), let g(x) be equal to y. Then, interchange y and x for each other and make y the subject of formula

Y = 3x + 3

X = 3y + 3

Make y the subject of formula

3y = x - 3

Y = x/3 - 3/3

Y = x/3 - 1

Therefore, g'(x) = x/3 - 1

For g'(12), substitute 12 for x in g' (x)

g'(x) = 12/4 - 1

g'(x) = 3 - 1

g'(x) = 2.

5 0

3 years ago

In the given figure, find m∠RST, if m∠RSU = 43º and m∠UST = 23º.

pickupchik [31]

Applying the angle addition postulate, the measure of angle RST is: 66°.

<h3>What is the Angle Addition Postulate?</h3>

If two angles share a common vertex and a common side, they are adjacent angles that form a larger angle. According to the angle addition postulate, the sum of these two adjacent angles will give a sum that is equal to the measure of the larger angle they both form.

We know the following:

Measure of angle RSU = 43º

Measure of angle UST = 23º

In the diagram given, angle RSU and angle UST are adjacent angles that form a larger angle, angle RST.

Therefore, based on the angle addition postulate, the measure of angle RST = sum of the measures of angles RSU and UST.

Therefore, we would have:

m∠RST = m∠RSU + m∠UST

Substitute

m∠RST = 43 + 23

m∠RST = 66°

Learn more about the angle addition postulate on:

brainly.com/question/24746945

#SPJ1

8 0

2 years ago

Determine whether each quadrilateral is a parallelogram. Justify your answer. Yes/No? Reason... opposite side congruent, opposit

Alex_Xolod [135]

Answer:

Yes! The given quadrilateral represents Parallelogram.

Reason: The given quadrilateral has opposite sides congruent.

Step-by-step explanation:

Given the quadrilateral with the four vertices.

Now in order to determine whether the given quadrilateral is a parallelogram or not, we need to check whether the opposite sides are congruent or not.