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schepotkina [342]
3 years ago
8

If a polynomial function f(x) has roots 3+Sqrt(5) and -6, what must be a factor of f(x)

Mathematics
1 answer:
neonofarm [45]3 years ago
5 0

Answer:

The two factors of the given polynomial f(x) are (x - 3 -√5) and (x +6) .

Step-by-step explanation:

Here, the roots of the given polynomial f(x)  are

Root 1  =  3 + √5

and  Root 2   =  (-6)

Now,as we know that if x  = a is the root of the any given polynomial p(x), then the expression (x-a) is the FACTOR of the polynomial p(x).

Now, here root 1 : x  = 3 + √5

So, x  - (3 + √5 ) is the FACTOR of the f(x)

or, ( x - 3 -√5) is the   first factor of f(x).

Also, here root 2 : x  = (-6)

So, x  - (-6 )   = x + 6   is the FACTOR of the f(x)

or, ( x +6 ) is the second factor of f(x).

Hence, the two factors of the given polynomial f(x)

are ( x - 3 -√5) and  ( x +6 ) .

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Show solutions please
slega [8]

Answer:

1. Their ages are:

Steve's age = 18

Anne's age = 8

2. Their ages are:

Max's age = 17

Bert's age = 11

3. Their ages are:

Sury's age = 19

Billy's age = 9

4. Their ages are:

The man's age = 30

His son's age = 10

Step-by-step explanation:

1. We make the assumption that:

S = Steve's age

A = Anne's age

In four years, we are going to have:

S + 4 = (A + 4)2 - 2 = 2A + 8 - 2

S + 4 = 2A + 6 .................. (1)

Three years ago, we had:

S - 3 = (A - 3)3

S - 3 = 3A - 9

S = 3A - 9 + 3

S = 3A – 6 …………. (2)

Substitute S from (2) into (1) and solve for A, we have:

3A – 6 + 4 = 2A + 6

3A – 2A = 6 + 6 – 4

A = 8

Substitute A = 8 into (3), we have:

S = (3 * 8) – 6 = 24 – 6

S = 18

Therefore, we have:

Steve's age = 18

Anne's age = 8.

2. We make the assumption that:

M = Max's age

B = Bert's age

Five years ago, we had:

M - 5 = (B - 5)2

M - 5 = 2B - 10 .......................... (3)

A year from now, it will be:

(M + 1) + (B + 1) = 30

M + 1 + B + 1 = 30

M + B + 2 = 30

M = 30 – 2 – B

M = 28 – B …………………… (4)

Substitute M from (4) into (3) and solve for B, we have:

28 – B – 5 = 2B – 10

28 – 5 + 10 = 2B + B

33 = 3B

B = 33 / 3

B = 11

If we substitute B = 11 into equation (4), we will have:

M = 28 – 11

M = 17

Therefore, their ages are:

Max's age = 17

Bert's age = 11.

3. We make the assumption that:

S = Sury's age

B = Billy's age

Now, we have:

S = B + 10 ................................ (5)

Next year, it will be:

S + 1 = (B + 1)2

S + 1 = 2B + 2 .......................... (6)

Substituting S from equation (5) into equation (6) and solve for B, we will have:

B + 10 + 1 = 2B + 2

10 + 1 – 2 = 2B – B

B = 9

Substituting B = 9 into equation (5), we have:

S = 9 + 10

S = 19

Therefore, their ages are:

Sury's age = 19

Billy's age = 9.

4. We make the assumption that:

M = The man's age

S = His son's age

Therefore, now, we have:

M = 3S ................................... (7)

Five years ago, we had:

M - 5 = (S - 5)5

M - 5 = 5S - 25 ................ (8)

Substituting M = 3S from (7) into (8) and solve for S, we have:

3S - 5 = 5S – 25

3S – 5S = - 25 + 5

-2S = - 20

S = -20 / -2

S = 10

Substituting S = 10 into equation (7), we have:

M = 3 * 10 = 30

Therefore, their ages are:

The man's age = 30

His son's age = 10

3 0
3 years ago
Plz help. Thank youuu
Natalija [7]

Answer:

c

Step-by-step explanation:

cause

3 0
2 years ago
1. 2 4/5v-2/3(4v+1 1/6)
Lerok [7]
1. -48v-5/45     2.44-r/2     3.  x=2
6 0
3 years ago
Read 2 more answers
After receiving his allowance, Spencer spent half of it on a Mother’s Day card. He bought two toy cars for $.49 each to give to
Lynna [10]
.49(2)+0.35+0.42= $1.75
7 0
3 years ago
7/10 ÷ 1/5 <br> pls i need help
blondinia [14]
7/10 ÷ 1/5 = 3 1/2 because if you just find the reciprocal of the second number (in this case 1/5) and then simply multiply the two numbers straight across after you find the reciprocal, you will need to convert and simplify as needed, and then you get your answer.
3 0
3 years ago
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