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2 years ago

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Determine the leading coefficient of the polynomial p, which has exactly three roots: -1, 1 and 2, and for which p(3) = 24 is tr

ue.

1 answer:

LuckyWell [14K]2 years ago

6 0

Answer:

The polynomial is $x^3-2x^2-x+2$

Leading coefficient is 1

Step-by-step explanation:

We need to determine the leading coefficient of polynomial p having roots

-1,1 and 2 and p(3)=24

Roots of polynomial are: -1,1,2

We can write them as:

x=-1, x=1, x=2

x+1=0, x-1=0, x-2=0

or:

(x+1)(x-1)(x-2)=0

Multiplying the terms to find the polynomial:

$(x+1)(x-1)(x-2)=0\\(x(x-1)+1(x-1))(x-2)=0\\(x^2-x+x-1)(x-2)=0\\(x^2-1)(x-2)=0\\x^2(x-2)-1(x-2)=0\\x^3-2x^2-x+2=0$

So, The polynomial is $x^3-2x^2-x+2$

The leading coefficient is the coefficient with highest power So, in polynomial we have highest power $x^3$ so, leading coefficient is 1

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Find the area of the triange below<br><br>units given are cm, cm^2, cm^3

notsponge [240]

Answer:

$A=150\ cm^2$

Step-by-step explanation:

The Hypotenuse of triangle, H = 25 cm

Base = 15 cm

Height = 20 cm

We need to find the area of the triangle. The area of a right-angled triangle is given by :

$A=\dfrac{1}{2}\times b\times h\\\\A=\dfrac{1}{2}\times 15\times 20\\A=150\ cm^2$

So, the area of the triangle is equal to $150\ cm^2$ .

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3 years ago

Liliana is making a vase with a circular base. She wants the area of the base to be between 135 cm2 and 155 cm2. Which circle co

Umnica [9.8K]

Answer:

(b) Circle C is shown. Line segment A C is a radius with length 7 centimeters.

Step-by-step explanation:

Given

$Minimum\ Area = 135cm^2$

$Maximum\ Area = 155cm^2$

$\pi = 3.14$

Required

Which circle could she use

To do this, we simply calculate the areas of all the given circles

The area of a circle is:

$Area = \pi r^2$

Where

$r = radius$

$a.\ r = 6cm$

The area is calculated as thus:

$Area = \pi r^2$

$Area = 3.14 * (6cm)^2$

$Area = 3.14 * 36cm^2$

$Area = 114.04cm^2$

$b.\ r = 7cm$

The area is calculated as thus:

$Area = \pi r^2$

$Area = 3.14 * (7cm)^2$

$Area = 3.14 * 49cm^2$

$Area = 153.86cm^2$

<em></em>

$c.\ r = 8cm$

The area is calculated as thus:

$Area = \pi r^2$

$Area = 3.14 * (8cm)^2$

$Area = 3.14 * 64cm^2$

$Area = 200.96cm^2$

$d.\ r = 9cm$

The area is calculated as thus:

$Area = \pi r^2$

$Area = 3.14 * (9cm)^2$

$Area = 3.14 * 81cm^2$

$Area = 254.34cm^2$

<em>From the calculations above; only the circle in option (b) has an area within the required range of 135 to 155cm^2</em>

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alexgriva [62]

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3 years ago

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Nataly_w [17]

Answer:

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Step-by-step explanation:

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