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dem82 [27]
3 years ago
10

Find the zeros for each function

Mathematics
1 answer:
iogann1982 [59]3 years ago
5 0

9514 1404 393

Answer:

  1. zeros are -10, and -1 (multiplicity 2)
  2. zeros are {-3, -2, 1, 3}

Step-by-step explanation:

For higher-degree polynomials I find it extremely useful to use a graphing calculator to find the zeros.

The usual approaches are ...

  • use the rational root theorem
  • try values of x=±1
  • narrow the search using Descartes' rule of signs
  • estimate maximum or minimum root values

__

1. Rational roots will be factors of 10, so ±1, ±2, ±5, or ±10. The signs are all positive, so there are no positive real roots. The sum of odd-degree coefficients is the same as the sum of even-degree coefficients, so -1 is one of the roots. Removing that using synthetic division gives you ...

   f(x) = (x +1)(x^2 +11 +10)

The quadratic (more or less obviously) factors as (x+1)(x+10), so the complete factorization is ...

  f(x) = (x +1)^2(x +10)

and the zeros are {-10, -1, -1}.

__

2. Rational roots will be factors of 18, so will be ±1, ±2, ±3, ±6, ±9, ±18. The sum of coefficients is 0, so x=1 is a root. The rule of signs tells you that there are 2 positive real roots, so there is one more positive real root. Synthetic division tells you the factoring so far is ...

  f(x) = (x -1)(x^3 +2x^2 -9x -18)

We note that the first two coefficients have the same ratio as the last two, so we can factor by grouping.

  x^3 +2x^2 -9x -18 = x^2(x +2) -9(x +2) = (x^2 -9)(x +2)

Factoring the difference of squares gives you the complete factorization, hence all of the roots. (The zeros are the values of x that make the factors zero.)

  f(x) = (x -1)(x +2)(x -3)(x +3)

The zeros are {-3, -2, 1, 3}.

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Answer:

The correct option is option B. It has one solution, and it's x=-3

Step-by-step explanation:

We have the following system of equations:

5x+7 = 2y                        (1)

y-9x=23                            (2)

Step 1: Solve for 'y' in equation (2):

y-9x = 23

y = 9x + 23

Step 2: Substitute in equation (1):

5x + 7 = 2y

5x + 7 = 2(9x + 23)

5x + 7 = 18x + 46

Step 3: Solve for x:

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Find the transition matrix from B to B'. B = {(-1,2), (3, 4)), B' = {(1, 0), (0, 1)} STEP 1: Begin by forming the following matr
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Answer:  The required matrix is

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Step-by-step explanation:  We are given to find the transition matrix from the bases B to B' as given below :

B = {(-1,2), (3, 4)) and B' = {(1, 0), (0, 1)}.

Let us consider two real numbers a, b such that

(-1,2)=a(1,0)+b(0,1)\\\\\Rightarrow (-1,2)=(a,b)\\\\\Rightarrow a=-1,b=2.

Again, let us consider reals c and d such that

(3,4)=c(1,0)+d(0,1)\\\\\Rightarrow (3,4)=(c,d)\\\\\Rightarrow c=3,d=4.

Therefore, the transition matrix is given by

T=\left[\begin{array}{ccc}-1&3\\2&4\end{array}\right] .

Thus, the required matrix is

T=\left[\begin{array}{ccc}-1&3\\2&4\end{array}\right] .

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See Explanation

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Let the temperatures of Miami and Bangor be M and B degrees respectively.

According to the given information:

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