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True [87]
3 years ago
6

These roots of the polynomial equation x^4-4x^3-2x^2+12x+9=0 are 3,-1,-1. Explain why the fourth root must be a real number. Fin

d the fourth root.
Mathematics
2 answers:
Svetradugi [14.3K]3 years ago
8 0

Answer:

Must be real because non real roots occur in pairs.

4th root = 3

Step-by-step explanation:

It must be real because complex roots occur only in conjugate pairs.

because of the  + 9  in the polynomial the 4th root will be 9 / (3*-1*-1) = 9/3 = 3

Alex787 [66]3 years ago
4 0

Roots with imaginary parts always occur in conjugate pairs. Three of the four roots are known and they are all real, which means the fourth root must also be real.

Because we know 3 and -1 (multiplicity 2) are both roots, the last root r is such that we can write

x^4-4x^3-2x^2+12x+9=(x-3)(x+1)^2(x-r)

There are a few ways we can go about finding r, but the easiest way would be to consider only the constant term in the expansion of the right hand side. We don't have to actually compute the expansion, because we know by properties of multiplication that the constant term will be (-3)(1)(1)(-r)=3r.

Meanwhile, on the left hand side, we see the constant term is supposed to be 9, which means we have

3r=9\implies r=3

so the missing root is 3.

Other things we could have tried that spring to mind:

- three rounds of division, dividing the quartic polynomial by (x-3), then by (x+1) twice, and noting that the remainder upon each division should be 0

- rational root theorem

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Answer:

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<em>Step-by-step explanation:</em>

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5 0
3 years ago
Janelle has a babysitting job for the sunumer. She works from 7 AM to 2 P.M. with a 30-minute, unpaid break in the middle of the
shtirl [24]

Answer: $146.25

Step-by-step explanation:

To solve the question, we need to first calculate the number of hours between 7 AM to 2 P.M which is 7 hours but we are told that there is a 30 minutes break. Therefore, he works for 6 hours 30 minutes which is 6 1/2 hours.

She's paid $4.50 pee hour, therefore the amount paid per day will be:

= 6 1/2 × $4.50

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7 0
3 years ago
I dont know the answer
Oduvanchick [21]
4/13 because the absolute value would be itself since it is positive. If it was negative then the absolute value would be positive.
8 0
3 years ago
the expression 6x +15 represents the total cost of a bicycle rental. When Danny rents a bike for 2 hours the total cost is 27 do
bekas [8.4K]

The coefficient 6 represents the price for an hour of bike rental.

3 0
3 years ago
What is the solution to the equation −p − 13 = −4 /3 p + 2/3 ( 5p − 6 ) ?
jekas [21]

Answer:

The answer is p= 2 and 1/3

Step-by-step explanation:

This answer can be found using the order of operations to solve for p.

Start by distributing 2/3 by (5p-6)

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subtract 13 from both sides

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3 0
2 years ago
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