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3 years ago

Given: f(x) = 2(x + 1)2 - 5

Mathematics

1 answer:

kirza4 [7]3 years ago

8 0

1. upwards
2. minimum -5
3. domain : xER range: y > -5
4) 2x^2 + 4x - 3

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Based on the Fundamental Theorem of Algebra, how many complex roots does each of the following equations have? Write your answer

Galina-37 [17]

According to the fundamental theorem of algebra, every polynomial of degree n has n complex zeroes.

Part A:

Given

$x(x^2-4)(x^2+16)=0 \\ \\ \Rightarrow x(x^4+12x^2-64)=0 \\ \\ \Rightarrow x^5+12x^3-64x=0$

Thus, the given polynomial is of degree 5 and hence has 5 omplrex roots.

Part B:

Given

$(x^2+4)(x+5)^2 = 0 \\ \\ \Rightarrow(x^2+4)(x^2+10x+25)=0 \\ \\ \Rightarrow x^4+10x^3+25x^2+4x^2+40x+100=0 \\ \\ \Rightarrow x^4+10x^3+29x^2+40x+100=0$

Thus, the polynomial is of degree 4 and hence has 4 complex roots.

Part C:

Given

$x^6-4x^5-24x^2+10x-3=0$

Thus, the given polynomial is of degree 6 and hence has 6 complex roots.

Part D:

Given

$x^7+128=0$

Thus, the given polynomial is of degree 7 and hence has 7 complex roots.

Part E:

Given

$(x^3+9)(x^2-4)=0 \\ \\ \Rightarrow x^5-4x^3+9x^2-36=0$

Thus, the given polynomial is of degree 5 and hence has 5 complex roots.

4 0

3 years ago

What is 2 1/4 cups converted to pints

DiKsa [7]

Answer:

1.125 0r 2.25

Step-by-step explanation:

the first is liquid and the second is cups

7 0

2 years ago

Some kids like to ride their bikes to and from school. Let d be the distance in miles from a kidʼs home to school. Write 2 expre

Elena L [17]

Answer:

x= amount of times that these kids ride their bikes to school in a week

D = total distance

w = weeks

Step-by-step explanation:

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4 years ago

Please help me please

kozerog [31]

Answer:

60°

Step-by-step explanation:

The radius of the circle is given as 7 ( centre of circle to point C )

The other radius is also 7 ( from centre to point D)

CD = 7

The triangle is therefore equilateral ( all 3 sides = 7 )

The angles of an equilateral triangle are equal and measure 60°

Hence mCD = 60°

8 0

4 years ago

I need help pleaseeee

zlopas [31]

Answer:

150

Step-by-step explanation:

30 to 31 days is in a month so its 150 because loook at the days.

8 0

3 years ago