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DerKrebs [107]
3 years ago
9

Find the polynomial with real coefficients, smallest possible degree, leading coefficient 1, such that 2 and 3+i are zeroes of t

he polynomial.
Mathematics
1 answer:
Bezzdna [24]3 years ago
6 0

f(x) = x³ - 8x² + 22x - 20

given x = a, x = b are zeros of a polynomial then

(x - a) and (x - b) are factors and the polynomial is the product of the factors

f(x) = k(x - a)(x - b) → ( k is a multiplier )

note that complex zeros occur in conjugate pairs

3 + 1 is a zero then 3 - i is a zero

zeros are x = 2, x = 3 + i and x = 3 - i, thus

(x - 2 ),(x - (3 + i )) and (x - (3 - i )) are the factors

f(x) = (x - 2)(x - 3 - i )(x - 3 + i)

     = (x - 2)(x² - 6x + 10)

     = x³ - 8x² + 22x - 20


   




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Abby filled her goodie bags with 4 cookies and 3 candy bars and spent a total of $10.25 per bag. Marissa filled her goodie bags
Leona [35]

Answer: See explanation

Step-by-step explanation:

The information given in the question can be presented into an equation as:

4x + 3y = 10.25 ...... equation i

2x + 7y = 14.75 ........ equation ii

Multiply equation i by 2

Multiply equation ii by 4

8x + 6y = 20.50 ...... equation iii

8x + 28y = 59 ...... equation iv

Subtract equation iii from iv

22y = 39.50

y = 39.50/22

y = 1.80

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From equation i

4x + 3y = 10.25

4x + 3(1.80) = 10.25

4x + 5.40 = 10.25

4x = 10.25 - 5.40

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x = 4.85/4

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4 0
3 years ago
Solve the 2x^2 - 5 = 13
DochEvi [55]

Answer:

x=3

x=−3

Step-by-step explanation:

2x^2 - 5 = 13

Subtract 13 from both sides.

2x^2 - 5 - 13 = 0

Subtract 13 from −5 to get −18.

2x^2 - 18 = 0

Divide both sides by 2.

x^2 - 9 = 0

Consider x^2−9. Rewrite x^2−9 as x^2−3^2. The difference of squares can be factored using the rule: a^2−b^2=(a−b)(a+b).

(x−3)(x+3)=0

To find equation solutions, solve x−3=0 and x+3=0.

x=3

x=−3

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3 years ago
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deff fn [24]

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Step-by-step explanation:

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3 years ago
What is angle m1, m2 and m3?
Vladimir [108]
M1 = 100
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