1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Oduvanchick [21]
3 years ago
10

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
Help help help help help
nekit [7.7K]

Answer:

C, C is the answer

5 0
3 years ago
......................................................................................................
antiseptic1488 [7]
The answer to your question is .........
5 0
3 years ago
p varies jointly as q and the square of r, and p = 200 when q = 2 and r = 3. Find p when q = 5 and r= 2.
Margarita [4]

Step-by-step explanation:

If a variables varies jointly, we can just divide it by the other variables in relation to it.

For example, since p variables jointly as q and square of r, then

\frac{p}{q {r}^{2} }  = k

where k is a constant

First, let find k. Substitute p= 200

q= 2, and r=3.

\frac{200}{2(3) {}^{2} }  = k

\frac{200}{18}  = k

\frac{100}{9}  = k

Now, since we know our constant, let find p.

\frac{p}{q {r}^{2} }  =  \frac{100}{9}

Q is 5, and r is 2.

\frac{p}{5( {2}^{2}) }  =  \frac{100}{9}

\frac{p}{20}  =  \frac{100}{9}

p =  \frac{2000}{9}

3 0
1 year ago
Given the function h(x)=-x^2-5x+14 determine the average rate of change of the function over the interval -9
Juli2301 [7.4K]

Answer:

The average rate of change of the function over the interval is of 6.

Step-by-step explanation:

Average rate of change:

The average rate of change of a function h(x) over an interval [a,b] is given by:

A = \frac{h(b)-h(a)}{b-a}

In this question:

Over the interval [-9,-2], so a = -9, b = -2, b - a = -2 -(-9) = 7

The function is:

h(x) = -x^2 - 5x + 14

h(-9) = -9^2 -5(-9) + 14 = -81 + 45 + 14 = -22

h(-2) = -2^2 -5(-2) + 14 = -4 + 10 + 14 = 20

Then

A = \frac{h(-2)-h(-9)}{7} = \frac{20-(-22)}{7} = \frac{42}{7} = 6

The average rate of change of the function over the interval is of 6.

8 0
3 years ago
-1/2x-1/4(10x-9)=-(-7/4x+2)-x
Tems11 [23]

Answer:

x= 17/15

Step-by-step explanation:

−1/2 x- 1/4 (10x−9)=−( -7/4 x+2)−x

8 0
3 years ago
Read 2 more answers
Other questions:
  • How to u estimate this<br> 5624 divided by 72
    6·1 answer
  • Solve for x in the equation? <br><br> a/(2x-c) = -1
    11·2 answers
  • a map shows the town where niko lives. the actual distance from niko's house to his school is 3miles, and measures one-half inch
    14·2 answers
  • Identify the recursive formula for the sequence 20, 28, 36, 44,.
    11·1 answer
  • (–3)^5<br><br><br><br> What does the ^ mean? Multiplication?
    11·2 answers
  • What is the area of a circle that has the diameter of 4?
    12·2 answers
  • A children's pool contains 17,500 milliliters. How many liters are in the pool
    13·1 answer
  • the relationship between the elapsed time in minutes since the stew was removed from the stove and temperature of the stew measu
    12·1 answer
  • Idk how to do this without an image honestly
    14·1 answer
  • Starasia says “My hair is 40 inches long, give or take 0.2 inches.” What is the percent error of the length of her hair?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!