All categories

3 years ago

Which of the following represents the zeros of f(x) = 6x3 − 31x2 + 4x + 5?

Mathematics

2 answers:

olga2289 [7]3 years ago

5 0

Answer: The correct option is

(B) 5, − one third , one half.

Step-by-step explanation: We are given to select the correct option that represents the zeroes of the following cubic function :

$f(x)=6x^3-31x^2+4x+5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We know that

if for any number a, the function f(x) is zero at x =a , then x = a is a zero of the function f(x).

We have, for the given function, at x = 5,

$f(5)\\\\=6\times5^3-31\times5^2+4\times5+5\\\\=125\times6-31\times25+20+5\\\\=750-775+25\\\\=0$

So, x = 5 is a zero of the function f(x).

Now, we have

$f(x)\\\\\=6x^3-31x^2+4x+5\\\\=6x^2(x-5)-x(x-5)-(x-5)\\\\=(x-5)(6x^2-x-1)\\\\=(x-5)(6x^2-3x+2x-1)\\\\=(x-5)(3x(2x-1)+1(2x-1))\\\\=(x-5)(3x+1)(2x-1)$

The zeroes of f(x) are given by

$f(x)=0\\\\\Rightarrow (x-5)(3x+1)(2x-1)=0\\\\\Rightarrow x-5=0,~~3x+1=0,~~2x-1=0\\\\\Rightarrow x=5,-\dfrac{1}{3},\dfrac{1}{2}.$

Thus, the zeroes of f(x) are 5, -one-third, one half.

Option (B) is CORRECT.

Butoxors [25]3 years ago

4 0

Answer:

5, − one third , one half

Step-by-step explanation:

If the number 'n' is a zero of f(x), then f(n)=0.

We could solve this problem by factorizing the polynomial, but the quickest way is by plugging the options into the equation.

We know that f(x) = 6x3 − 31x2 + 4x + 5.

Then:

f(-5) ≠ 0

f(1/3) ≠ 0

f(-1/2) ≠ 0

f(5) = 0

f(-1/3) = 0

f(1/2) = 0

Then, the correct option is: 5, − one third , one half.

Finally, the factorized form is: (x−5)(2x−1)(3x+1). If you expand it, you will get the original polynomial.

You might be interested in

A researcher wants to construct a 90% confidence interval for the proportion of elementary school students in Seward County who

dezoksy [38]

Answer:

The sample size is $n =68$

Step-by-step explanation:

The population proportion is $\^ p = 0.50$

The margin of error is $E = 0.1$

From the question we are told the confidence level is 90% , hence the level of significance is

$\alpha = (100 - 90 ) \%$

=> $\alpha = 0.10$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.645$

Generally the sample size is mathematically represented as

$n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p )$

=> $n = [\frac{1.645 }{0.1} ]^2 * 0.50 (1 - 0.50 )$

=> $n =68$

6 0

3 years ago

Hunter took out a $3500 loan with interest to pay for some business supplies. He will repay The loan and three years with monthl

almond37 [142]

Answer: $448.48

Step-by-step explanation:

The amount Hunter will pay in total is;

= 109.68 * 12 months * 3 years

= $‭3,948.48‬

Interest he will pay = Amount paid - Loan amount

= ‭3,948.48‬ - 3,500

= $448.48

7 0

3 years ago

Cone A has a diameter of 12 meters and a slant height of 9 meters. The linear dimensions of cone B are 5 times the linear dimens

Karolina [17]

Answer:

Cone volume formula

To calculate its volume you need to multiply the base area (area of a circle: π * r²) by height and by 1/3: volume = (1/3) * π * r² * h

Step-by-step explanation:

8 0

3 years ago

PLEASE HELP ME. NO PHONY ANSWERS TY, ANSWER IF YOUR 100% RIGHT!

Ksivusya [100]

The relative frequency of female mathematics majors will be 0.5142.

<h3>How to find the relative frequency?</h3>

The proportion of the examined subgroup's value to the overall account is known as relative frequency.

A sample of 317 students at a university is surveyed.

The students are classified according to gender (“female” or “male”).

The table is given below.

Then the relative frequency of female mathematics majors will be

⇒ 36 / (36 + 34)

⇒ 36 / 70

⇒ 0.5142

Learn more about conditional relative frequency here:

brainly.com/question/8358304

#SPJ1

8 0

2 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:

$Area = \pi r^2$

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

$Area = 3.14 * 49cm^2$

$Area = 153.86cm^2$

$c.\ r = 8cm$

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>

6 0

3 years ago

Read 2 more answers