Cameron bought four begonias in 6-in pots and a $19 fern at a fundraiser. he spent a total of $63. how much is each begonia?

If a polynomial function f(x) has roots -8, 1, and 6i, what must also be a root of f(x)?

Naddik [55]

Answer:

it must also have the root : - 6i

Step-by-step explanation:

If a polynomial is expressed with real coefficients (which must be the case if it is a function f(x) in the Real coordinate system), then if it has a complex root "a+bi", it must also have for root the conjugate of that complex root.

This is because in order to render a polynomial with Real coefficients, the binomial factor (x - (a+bi)) originated using the complex root would be able to eliminate the imaginary unit, only when multiplied by the binomial factor generated by its conjugate: (x - (a-bi)). This is shown below:

$(x-(a+bi))*(x-(a-bi))=\\(x-a-bi)*(x-a+bi)=\\([x-a]-bi)*([x-a]+bi)=\\(x-a)^2-(bi)^2=\\(x-a)^2-b^2(-1)=\\(x-a)^2+b^2$

where the imaginary unit has disappeared, making the expression real.

So in our case, a+bi is -6i (real part a=0, and imaginary part b=-6)

Then, the conjugate of this root would be: +6i, giving us the other complex root that also may be present in the real polynomial we are dealing with.

5 0

3 years ago

What is the ratio a:b if 8a=3b?

Digiron [165]

The ratio a:b is 3:8

Step-by-step explanation:

In simple words, the ratio a:b means the fraction a/b.

So we will have to solve the given equation for a/b

Given

$8a=3b$

Dividing both sides by 8

$\frac{8a}{8}=\frac{3b}{8}\\a=\frac{3b}{8}$

Dividing both sides by b

$\frac{a}{b}=\frac{3b}{8*b}\\\frac{a}{b} =\frac{3}{8}$

The ratio a:b is 3:8

Keywords: Ratios, Fractions

Learn more about ratios at:

#LearnwithBrainly

5 0

3 years ago

Select all of the expression that are equivalent to 4(3x + 14y)

ASHA 777 [7]

Answer:

12x + 64y

Step-by-step explanation:

This is the distributed property. You need to apply it according to this question

8 0

3 years ago

The LaSalle High School senior class raised funds for an end of the year cruise getaway. The city gave them a special package fo

harkovskaia [24]

45 students is the answer to the question

8 0

3 years ago

Read 2 more answers

Jordan was asked to convert 345,000,000 to scientific notation. His response was 34.5*10^7. His teacher told him he was incorrec

mel-nik [20]

Step-by-step explanation:

The scientific notation of any number is given by :

$N=a\times 10^b$

a is any real no and b is any integer

The scientific notation of 345,000,000 should be $3.45\times 10^8$ but Jorden wrote 34.5×10⁷. He is incorrect. He should have shifted decimal before 4 such that power of 10 becomes 8.

5 0

3 years ago