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-BARSIC- [3]
3 years ago
12

Simplify the expression 2(6x + 3)

Mathematics
1 answer:
UNO [17]3 years ago
6 0
12x + 6 because 2 times 6 is 12 and 2 times 3 is 6
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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
Alex787 [66]

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

4 0
3 years ago
Read 2 more answers
Convert 36°F to degrees Celsius.
scoray [572]

Answer:

I think once you do the math you'd get 2.22 celsius.

Step-by-step explanation:

8 0
3 years ago
I need help for finding out what x is in the fraction. 3/x = 18/36
Vedmedyk [2.9K]

Answer:

x = 6

Step-by-step explanation:

3 / 6 = 18 / 36

3 × 6 = 18

6 x 6 = 36

6 0
3 years ago
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Please help. i don't understand what it's asking me to do
zavuch27 [327]

Answer:

B

Step-by-step explanation:

It's not telling us what to do with the data given. So it's most likely B.

7 0
3 years ago
Given (x – 7)2 = 36, whats the values of x
nata0808 [166]
<span>x = 25
(x – 7)2 = 36
(x*2) - (7*2) = 36 : multiply x*2 and 7*2 because of distributive property 
2x - 14 = 36 : multiply
2x = 36 + 14 : add 14 to combine like terms 
2x = 50 : add
x = 50/2 : divide 50 by 2 to get x alone
x = 25 : simplify </span>
4 0
3 years ago
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