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julia-pushkina [17]
3 years ago
9

What are the real zeros of the function g(x) = x3 + 2x2 − x − 2?

Mathematics
1 answer:
Nat2105 [25]3 years ago
4 0
Upon a slight rearrangement this problem gets a lot simpler to see.

x^3-x+2x^2-2=0  now factor 1st and 2nd pair of terms...

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

(x+2)(x^2-1)=0  now the second factor is a "difference of square" of the form:

(a^2-b^2) which always factors to (a+b)(a-b), in this case:

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

So g(x) has three real zero when x={-2, -1, 1}
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valentina_108 [34]
Set 7x-4 and 31 equal to each other
7X-4=31
Add four to both sides
7X=27
X=3
The answer is D
4 0
3 years ago
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Simplify<br> a(cube)-1000b(cube)<br> 64a(cube)-125b(cube)
Elanso [62]

The simplification of a³ - 1000b³ and 64a³ - 125b³ is (a - 10b) × (a² + 10ab + 100b²) and 4a - 5b) • (16a² + 20ab + 25b²) respectively.

<h3>Simplification</h3>

Question 1: a³ - 1000b³

a³ - b³

= (a-b) × (a² +ab +b²)

  • 1000 is the cube of 10
  • a³ is the cube of a¹
  • b³ is the cube of b¹

So,

(a - 10b) × (a² + 10ab + 100b²)

Question 2: 64a³ - 125b³

a³ - b³

= (a-b) × (a² +ab +b²)

  • 64 is the cube of 4
  • 125 is the cube of 5
  • a³ is the cube of a¹
  • b³ is the cube of b¹

So,

(4a - 5b) • (16a² + 20ab + 25b²)

Learn more about simplification:

brainly.com/question/723406

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8 0
2 years ago
david counts the quarters in his change jar. He has 24 more quarters than his brother Rob. if r is the number of quarters Rob ha
denis-greek [22]
Rob has R quarters, and David has R + 24 or 24 more than rob, so together they have 2R+24
8 0
3 years ago
Nolan has a bond with a 6.1% yield, a bid price of $475, and a face value of $500. What is the original coupon rate of this Bond
Vladimir79 [104]

Answer:

5.8%

Step-by-step explanation:

Current yield = 6.1%

Face value of bond = $500

Market price of bond = $475

Let the original coupon rate be CR

Current\hspace{2}yield = \frac{Coupon\hspace{2}rate* Bond\hspace{2}face\hspace{2}value}{Market\hspace{2}price}*100

6.1 = \frac{CR*500}{475}*100

Multiply both sides by 475

6.1 *475 = \frac{CR*500}{475}*100*475

Cancel out the 475's from the top and bottom of the right side

6.1 *475 = CR*500*100

2897.5 = CR*50000

Flip the sides

CR*50000 = 2897.5

Divide both sides by 5000

\frac{CR*50000}{50000} = \frac{2897.5}{50000}

Cancel out 50000 from the top and bottom of the left side

CR = 0.0579%

CR = 0.0579 * 100      [convert decimal into a percentage]

CR = 5.79 %

CR = 5.8% [rounded off to the tenth place]

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The factors of 49 are: 1, 7 and 49.
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