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3 years ago

If the polynomial p(X)=x⁴-2x³+x²-1 is divided by (X+1), then the degree of quotient polynomial.

Mathematics

1 answer:

Sergeeva-Olga [200]3 years ago

7 0

Answer:

Step-by-step explanation:

Cancel all out and you will get 3.

x+1/x⁴-2x³+x²-1

81-64+7-21=3

Hope this helps :D

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write a polynomial function of least degree with integral coefficients that has the given zeros. -(1/3), -i

inessss [21]

Answer:

$f(x)=3x^3+x^2+3x+1$

Step-by-step explanation:

If a real number $-\frac{1}{3}$ is a zero of polynomial function, then

$x-\left(-\dfrac{1}{3}\right)=x+\dfrac{1}{3}$

is the factor of this function.

If a complex number $-i$ is a xero of the polynomial function, then the complex number $i$ is also a zero of this function and

$x-(-i)=x+i\ \text{ and }\ x-i$

are two factors of this function.

So, the function of least degree is

$f(x)=\left(x+\dfrac{1}{3}\right)(x+i)(x-i)=\left(x+\dfrac{1}{3}\right)(x^2-i^2)=\\ \\ =\left(x+\dfrac{1}{3}\right)(x^2+1)=\dfrac{1}{3}(3x+1)(x^2+1)=\dfrac{1}{3}(3x^3+x^2+3x+1)$

If the polynomial function must be with integer coefficients, then it has a form

$f(x)=3x^3+x^2+3x+1$

4 0

4 years ago

A rectangular stained glass window is made up of identical triangular parts as pictured below.

Pachacha [2.7K]

36/4=9 48/3=16 so 9*16=144/2=72 so it is 72 square inches

3 0

3 years ago

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Under a translation of 5 units up and 2 units to the left, the point (3,4) will become

Vedmedyk [2.9K]

The point would become (8,2)
3+5=8
4-2=2

4 0

4 years ago

2.3 The diameter of a circle is 8 m long. Calculate its: radius

slavikrds [6]

Answer:

Step-by-step explanation:

Diameter is equal to 2r

so,

8÷2=4

4 0

3 years ago

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4C. Quintin is using the three different shaped

Sauron [17]

The smallest number of tiles Quintin will need in order to tile his floor is 20

The given parameters;

number of different shapes of tiles available = 3

number of each shape = 5

area of each square shape tiles, A = 2000 cm²

length of the floor, L = 10 m = 1000 cm

width of the floor, W = 6 m = 600 cm

To find:

the smallest number of tiles Quintin will need in order to tile his floor

Among the three different shapes available, total area of one is calculated as;

$A_{one \ square \ type} = 5 \times 2000 \ cm^2 = 10,000 \ cm^2$

Area of the floor is calculated as;

$A_{floor} = 1000 \ cm \times 600 \ cm = 600,000 \ cm^2$

The maximum number tiles needed (this will be possible if only one shape type is used)

$maximum \ number= \frac{Area \ of \ floor}{total \ area \ of \ one \ shape \ type} \\\\maximum \ number= \frac{600,000 \ cm^2}{10,000 \ cm^2} \\\\maximum \ number= 60$

When all the three different shape types are used we can get the smallest number of tiles needed.

The minimum or smallest number of tiles needed (this will be possible if all the 3 different shapes are used)

$3 \times \ smallest \ number = 60\\\\smallest \ number = \frac{60}{3} \\\\smallest \ number = 20$

Thus, the smallest number of tiles Quintin will need in order to tile his floor is 20

Learn more here: brainly.com/question/13877427

3 0

3 years ago