X^2-14x+ 58 = 0
A. (3+ 7i,3 - 7i)
B. (2+19i,2 - 19i)
c. (2+9i,2 - 9i)
D. (7+3i,7-3i)

9514 1404 393

 D.  7 +3i, 7 -3i

Step-by-step explanation:

When the leading coefficient of the quadratic is 1, as it is here, the sum of the roots is equal to the opposite of the coefficient of the x-term. So, we need the sum of roots to be -(-14) = 14.

In each case, the imaginary parts cancel when the roots are added. The real parts of the roots are the same, so the sum of roots is double the real part of one of the roots. In order for that to be 14, the real part of the root must be 7.

Only answer choice D matches this requirement.

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Algebraic solution

  x^2 -14x +58 = 0 . . . . given

  (x -7)^2 = -9 . . . . . . . subtract 9 and write as a square

  x = 7 ± 3i . . . . . . . . square root and add 7

Additional comment

When p and q are roots, (x-p) and (x-q) are factors. The expansion of the factored form is ...

  (x -p)(x -q) = x^2 -(p+q)x +pq = 0

That is, the constant term is the product of the roots, and the linear (x) term coefficient is the opposite of the sum of the roots. This can help you check quickly if an offered choice of roots is applicable to the given equation. This is also the basis of the thinking used to factor the equation.

step-by-step explanation:

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range: