2 years ago

HELP PLS I WILL GIVE BRAINLIEST. NO LINKS!!!

1 answer:

8 0

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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.

Lelechka [254]

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

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

4 0

2 years ago

A faucet can fill a bathtub in 6 minutes. the drain can empty the tub in 10 minutes. If both the faucets and the drain are open

Zepler [3.9K]

Answer:

4t/15

Step-by-step explanation:

Please trust me

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2 years ago

PLZ HELP

charle [14.2K]

Answer:

17 pants and 9 shirts

let x rep pants

let y rep shirts

x + y =26

225 x + 125 y =4950

x = 26 - y

225(26 - y) + 125y= 4950

5850-225y+125y = 4950

5850-100y=4950

-100y=4950-5850

-100y=-900

y=9

x = 26 - (9)

x = 17

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2 years ago

Ax+by=c What is the equivalent equation

kenny6666 [7]

Ax plus BY equals C.

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2 years ago

PLEASE HELP ALGEBRA 1 QUESTION

WITCHER [35]

I think it would be the first answer.

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3 years ago