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gayaneshka [121]
2 years ago
15

The polynomial function y = x3 -3x2 + 16x - 48 has only one non-repeated x-intercept. What do you know about the complex zeros o

f the function?
A)
The function has one imaginary zero.


B)
The function has one real zero and two imaginary zeros.


C)
The function has one real zero and one imaginary zero.


D)
The function has one imaginary zero and two real zeros.
Mathematics
1 answer:
earnstyle [38]2 years ago
3 0
• First way to solve:
We'll manipulate the expression of the equation:

y=x^3-3x^2+16x-48\\\\ y=x^2(x-3)+16(x-3)\\\\ y=(x-3)(x^2+16)

If we have y=0:

x-3=0~~~or~~~x^2+16=0\\\\ x=3~~~or~~~x^2=-16\\\\ x=3~~~or~~~x=\pm\sqrt{-16}\\\\ x=3~~~or~~~x=\pm4i

Then, the function has one real zero (x=3) and two imaginary zeros (4i and -4i).

Answer: B


• Second way to solve:

The degree of the function is 3. So, the function has 3 complex zeros.

Since the coefficients of the function are reals, the imaginary roots are in a even number (a imaginary number and its conjugated)

The function "has only one non-repeated x-intercept", then there is only one real zero.

The number of zeros is 3 and there is 1 real zero. So, there are 2 imaginary zeros.

Answer: B.
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The angle θ lies in Quadrant II. sinθ=3/4 What is cosθ ?
Elden [556K]

Hello from MrBillDoesMath

Answer:

[email protected] = - sqrt(7)/ 4    

which is choice B

Discussion:

This problem can be solved by drawing triangles and looking at ratios of sides or by using the trig identity:

([email protected])^2 + (sin2)^2 = 1

If [email protected] = 3/4 , the

([email protected])^2 + (3/4)^2 = 1 =>              (subtract (3/4)^2 from both sides)

([email protected])^2 = 1 - (3/4)^2  = 1 - 9/16   = 7/16

So...... taking the square root of both sides gives

[email protected] =  +\- sqrt(7)/ sqrt(16) = +\- sqrt(7)/4

But is [email protected] positive or negative?  We are told that @ is in the second quadrant and cos(@) is negative in this quadrant, so our answer must be negative

[email protected] = - sqrt(7)/ 4    

which is choice B


Thank you,

Mr. B


4 0
3 years ago
Jackson says has an odd number of model cars.he has 6 cars on one shel and 8 cars on another shelf.is jackson correct?explain
grigory [225]
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I hope this helps! If not I'm sorry. 
4 0
3 years ago
Write the equation of the line MN, which is formed by the points M(-3,5) and N(2,0)
belka [17]
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3 0
3 years ago
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The faces on a number cube are labled 1,2,2,3,4, and 5the number cube is rolled 114 times how many times would you expect the nu
Mrac [35]

Given:

The faces on a number cube are labeled 1,2,2,3,4, and 5.

The number cube is rolled 114 times.

To find:

How many times would you expect the number 2 to appear?

Solution:

We have,

Total outcomes = 1,2,2,3,4, and 5.

Number of total outcomes = 6

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Number of favorable outcomes = 2

The probability of getting 2 is:

P(2)=\dfrac{\text{Number of favorable outcomes}}{\text{Number of total outcomes}}

P(2)=\dfrac{2}{6}

P(2)=\dfrac{1}{3}

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E(x)=114\times P(2)

E(x)=114\times \dfrac{1}{3}

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Therefore, the expected number of times is 38.

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2 years ago
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