If 5 + 6i is a root of the polynomial function f(x), which of the following must also be a root of f(x)? –5 – 6i 5 – 6i 6 – 5i 6 + 5i

5-6i

The rule is that if f(x) has real number coefficients, then a root of x = a+bi pairs up with its conjugate pair of x = a - bi. In this case, a = 5 and b = 6.

5 -6i is also the root of  f(x).

Step-by-step explanation:

Given : If 5 + 6i is a root of the polynomial function f(x),

To find  : which of the following must also be a root of f(x).

Solution : We have given that 5+6i is the on of the root of polynomial function f(x).

It has two parts real and imaginary  part so , it is a complex number .

Real part  = 5  and 6i is imaginary part.

Complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. For example, the complex conjugate of a + bi is a − bi.

a = 5 , b = 6.

Then by the complex conjugate defination , Another root would be 5 - 6i

Therefore, 5 -6i is also the root of  f(x).

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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a. turk and mcalister

b. howard, mission, and market

c. yes. since streets end some do not cross yet are not parallel to others. example: mcalister and 5th

step-by-step explanation:

parallel lines are lines which do not intersect ever and look a lot like railroad tracks. turk, mcalister and golden gate are examples of these.

intersect are streets which cross each other and a car on one can reach the other. howard, mission, and market intersect with 6th.

skew lines are lines which neither intersect nor are parallel. these lines exist here because some streets end and never intersect another like mcalister and 5th.