All categories

2 years ago

Find all of the x-intercepts of the polynomial function p(x) = 3x^3-23x^2+33x–5

Mathematics

1 answer:

kari74 [83]2 years ago

5 0

Answer:

x=5/3

x= 3+2 $\sqrt{2}$

x= 3-2 $\sqrt{2}$

Step-by-step explanation:

if graphed the x intercepts would be (5/3 , 0) (3+2 $\sqrt{2}$ ) (3-2 $\sqrt{2}$ )

y intercepts (0,-5)

You might be interested in

Factor out the GCF from the terms of the polynomial –4y5 + 6y3 + 8y2 – 2y. A. –2y4 + 3y2 + 4y – 1 B. y(–4y4 + 6y2 + 8y – 2) C. 2

andreyandreev [35.5K]

Answer:

Option D) $-2y(2y^4-3y^2-4y+1)$ is correct

Therefore $-4y^5+6y^3+8y^2-2y=-2y(2y^4-3y^2-4y+1)$

Step-by-step explanation:

Given polynomial is $-4y^5+6y^3+8y^2-2y$

To factorise the given polynomial by taking out the common terms of the given polynomial :

$-4y^5+6y^3+8y^2-2y$
$=2y(-2y^4+3y^2+4y-1)$ ( here 2y is GCF common term so taking outside the terms of the polynomial )
$=-2y(2y^4-3y^2-4y+1)$ ( now taking (-) outside )

Therefore $-4y^5+6y^3+8y^2-2y=-2y(2y^4-3y^2-4y+1)$

Option D) $-2y(2y^4-3y^2-4y+1)$ is correct

8 0

3 years ago

Find the zeros of the following polynomial functions, with their multiplicities. (a) f(x)= (x +1)(x − 1)(x² +1) (b) g(x) = (x −

larisa [96]

Answer:

a) zeros of the function are x = 1 and, x = -1

b) zeros of the function are x = 2 and, x = 4

c) zeros of the function are x = $\frac{3}{2}$

d) zeros of the function are x = $\frac{-4}{3}$ and, x = 17

Step-by-step explanation:

Zeros of the function are the values of the variable that will lead to the result of the equation being zero.

Thus,

a) f(x)= (x +1)(x − 1)(x² +1)

now,

for the (x +1)(x − 1)(x² +1) = 0

the condition that must be followed is

(x +1) = 0 ..........(1)

(x − 1) = 0 ..........(2)

(x² +1) = 0 ...........(3)

considering the equation 1, we have

(x +1) = 0

x = -1

for

(x − 1) = 0

x = 1

and,

for (x² +1) = 0

x² = -1

x = √(-1) (neglected as it is a imaginary root)

Thus,

zeros of the function are x = 1 and, x = -1

b) g(x) = (x − 4)³(x − 2)⁸

now,

for the (x − 4)³(x − 2)⁸ = 0

the condition that must be followed is

(x − 4)³ = 0 ..........(1)

(x − 2)⁸ = 0 ..........(2)

considering the equation 1, we have

(x − 4)³ = 0

x -4 = 0

x = 4

and,

for (x − 2)⁸ = 0

x - 2 = 0

x = 2

Thus,

zeros of the function are x = 2 and, x = 4

c) h(x) = (2x − 3)⁵

now,

for the (2x − 3)⁵ = 0

the condition that must be followed is

(2x − 3)⁵ = 0

2x - 3 = 0

2x = 3

x = $\frac{3}{2}$

Thus,

zeros of the function are x = $\frac{3}{2}$

d) k(x) =(3x +4)¹⁰⁰(x − 17)⁴

now,

for the (3x +4)¹⁰⁰(x − 17)⁴ = 0

the condition that must be followed is

(3x +4)¹⁰⁰ = 0 ..........(1)

(x − 17)⁴ = 0 ..........(2)

considering the equation 1, we have

(3x +4)¹⁰⁰ = 0

(3x +4) = 0

3x = -4

x = $\frac{-4}{3}$

and,

for (x − 17)⁴ = 0

x - 17 = 0

x = 17

Thus,

zeros of the function are x = $\frac{-4}{3}$ and, x = 17

7 0

3 years ago

The side s of a square carpet is measured at 5 ft. Estimate using the Linear Approximation the maximum error in the area A of th

KonstantinChe [14]

Answer:

$0.333 ft^2$

Step-by-step explanation:

We are given that

Side of square carpet,s=5 ft

$\Delta s=0.4 in=\frac{0.4}{12}ft$

1 foot=12 in

We have to find the maximum error in the area of the carpet by using the linear approximation .

Area of square,A= $(side)^2=s^2$

$dA=2sds$

Substitute the values

$dA=2\times 5\times \frac{0.4}{12}$

$dA=0.333ft^2$

Hence, the maximum error in the area of the carpet= $0.333 ft^2$

4 0

3 years ago

A rectangle with sides 12 cm and 14 cm has the same diagonal as a square.

adelina 88 [10]

Answer:

Length of side of square $=\sqrt{170}$

Step-by-step explanation:

Sides of rectangle $=12,14\ cm$

let $x$ be diagonal of rectangle

<u><em>Pythagorean theorem : The square of hypotenuse is equal to sum of square of sides.</em></u>

Here hypotenuse $=x$

$x^{2} =12^{2}+14^{2}\\x^{2} =144+196\\x^{2} =340\\x=\sqrt{340}$

Diagonal of square $=\sqrt{340}$

let side of square $=a$

again use pythagorean theorem

$340=a^{2}+a^{a}\\2a^{2}=340\\a^{2}=170\\a=\sqrt{170}$

8 0

3 years ago

Can someone help me please

RUDIKE [14]

Answer:

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Find all of the x-intercepts of the polynomial function p(x) = 3x^3-23x^2+33x–5​

Find all of the x-intercepts of the polynomial function p(x) = 3x^3-23x^2+33x–5