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Lesechka [4]
3 years ago
10

If α and β are the zeros of the quadratic polynomial f(x) = 3x2–4x + 5, find a polynomialwhose zeros are 2α + 3β and 3α + 2β.

Mathematics
1 answer:
Lelechka [254]3 years ago
4 0

Answer:

\boxed{\sf \ \ \ 3x^2-20x+37\ \ \ }

Step-by-step explanation:

Hello,

a and b are the zeros, we can say that

f(x)=3(x^2-\dfrac{4}{3}x+\dfrac{5}{3}) = 3(x-a)(x-b)=3(x-(a+b)x+ab)

So we can say that

a+b=\dfrac{4}{3}\\ab=\dfrac{5}{3}

Now, we are looking for a polynomial where zeros are 2a+3b and 3a+2b

for instance we can write

(x-2a-3b)(x-3a-2b)=x^2-(2a+3b+3a+2b)x+(2a+3b)(3a+2b)\\= x^2-5(a+b)x+6a^2+6b^2+9ab+4ab

and we can notice that

a^2+b^2=(a+b)^2-2ab so

(x-2a-3b)(x-3a-2b)=x^2-5(a+b)x+6[(a+b)2-2ab]+13ab\\= x^2-5(a+b)x+6(a+b)^2+ab

it comes

x^2-5*\dfrac{4}{3}x+6(\dfrac{4}{3})^2+\dfrac{5}{3}

multiply by 3

3x^2-20x+2*16+5=3x^2-20x+37

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<u>Answer:</u>

<h3>( x ) x ( x + 7 ) </h3>

<u>Step-by-step explanation:</u>

To find the area of a rectangle, we have to multiply the length with the width.

In the question, the given length is 'x' and the width given is 'x +7'

So, the area would be

( x ) x ( x + 7 )

The area = x^{2} + 7x

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( x ) x ( x + 7 )

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111 & 82

Step-by-step explanation:

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3 years ago
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Solve for j: J/-2+7=-12
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Answer:

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Step-by-step explanation:

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3 years ago
Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
Rzqust [24]

Answer:

a = 6 or 9

Step-by-step explanation:

The "a", "b", and "c" of the quadratic formula are the coefficients of a², a, and the constant term in the given equation:

... a = 2, b = -30, c = 108

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... = (-(-30) ± √((-30)² -4(2)(108)))/(2(2))

... = (30 ± √(900 -864))/4

... = (30 ± √36)/4

... = (30 ± 6)/4 = {24, 36}/4

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3 years ago
What is the output value of (4x+2)(x-5)/2 using input value of x=2
Firdavs [7]

Answer:

-15

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Step-by-step explanation:

<u>Step 1: Define</u>

(4x + 2)(x - 5) / 2

x = 2

<u>Step 2: Evaluate</u>

  1. Substitute:                             (4 · 2 + 2)(2 - 5) / 2
  2. Parenthesis - Multiply:          (8 + 2)(2 - 5) / 2
  3. Parenthesis - Add:                10(2 - 5) / 2
  4. Parenthesis - Subtract:         10(-3) / 2
  5. Multiply:                                 -30 / 2
  6. Divide:                                    -15
6 0
3 years ago
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