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Ilya [14]
2 years ago
14

Suppose a, b denotes of the quadratic polynomial x² + 20x - 2022 & c, d are roots of x² - 20x + 2022 then the value of ac(a

- c) ad(a - d) + bc(b - c) + (b - d)
Choose the correct option
(a) 0
(b) 8000
(c) 8080
(d) 16000​
Mathematics
1 answer:
Alja [10]2 years ago
4 0
<h3><u>Correct Question :- </u></h3>

\sf\:a,b \: are \: the \: roots \: of \:  {x}^{2} + 20x - 2020 = 0 \: and \:  \\  \sf \: c,d \: are \: the \: roots \: of \:  {x}^{2}  -  20x  + 2020 = 0 \: then \:

\sf \: ac(a - c) + ad(a - d) + bc(b - c) + bd(b - d) =

(a) 0

(b) 8000

(c) 8080

(d) 16000

\large\underline{\sf{Solution-}}

Given that

\red{\rm :\longmapsto\:a,b \: are \: the \: roots \: of \:  {x}^{2} + 20x - 2020 = 0}

We know

\boxed{\red{\sf Product\ of\ the\ zeroes=\frac{Constant}{coefficient\ of\ x^{2}}}}

\rm \implies\:ab = \dfrac{ - 2020}{1}  =  - 2020

And

\boxed{\red{\sf Sum\ of\ the\ zeroes=\frac{-coefficient\ of\ x}{coefficient\ of\ x^{2}}}}

\rm \implies\:a + b = -  \dfrac{20}{1}  =  - 20

Also, given that

\red{\rm :\longmapsto\:c,d \: are \: the \: roots \: of \:  {x}^{2}  -  20x  + 2020 = 0}

\rm \implies\:c + d = -  \dfrac{( - 20)}{1}  =  20

and

\rm \implies\:cd = \dfrac{2020}{1}  = 2020

Now, Consider

\sf \: ac(a - c) + ad(a - d) + bc(b - c) + bd(b - d)

\sf \:  =  {ca}^{2} -  {ac}^{2} +  {da}^{2} -  {ad}^{2} +  {cb}^{2} -  {bc}^{2} +  {db}^{2} -  {bd}^{2}

\sf \:  =  {a}^{2}(c + d) +  {b}^{2}(c + d) -  {c}^{2}(a + b) -  {d}^{2}(a + b)

\sf \:  = (c + d)( {a}^{2} +  {b}^{2}) - (a + b)( {c}^{2} +  {d}^{2})

\sf \:  = 20( {a}^{2} +  {b}^{2}) + 20( {c}^{2} +  {d}^{2})

\sf \:  = 20\bigg[ {a}^{2} +  {b}^{2} + {c}^{2} +  {d}^{2}\bigg]

We know,

\boxed{\tt{  { \alpha }^{2}  +  { \beta }^{2}  =  {( \alpha   + \beta) }^{2}  - 2 \alpha  \beta  \: }}

So, using this, we get

\sf \:  = 20\bigg[ {(a + b)}^{2} - 2ab +  {(c + d)}^{2} - 2cd\bigg]

\sf \:  = 20\bigg[ {( - 20)}^{2} +  2(2020) +  {(20)}^{2} - 2(2020)\bigg]

\sf \:  = 20\bigg[ 400 + 400\bigg]

\sf \:  = 20\bigg[ 800\bigg]

\sf \:  = 16000

Hence,

\boxed{\tt{ \sf \: ac(a - c) + ad(a - d) + bc(b - c) + bd(b - d) = 16000}}

<em>So, option (d) is correct.</em>

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Answer:

The correct option is;

The ratio of the area of the scale drawing to the area of the sign is equal to the square of the scale factor

Step-by-step explanation:

Here we have a scale factor of 1:8

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5 0
3 years ago
Lianne charged twice as much to walk a large dog than she did to walk a small dog. This week she had time to was 10 small dogs a
guapka [62]
Well she charged twice as much to walk large then small. Let s be small and l be large.
We we know that
l = 2s

we also know that she wants to make 100 so
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3 years ago
For some postive value of Z, the probability that a standardized normal variable is between 0 and Z is 0.3770. The value of Z is
Talja [164]

Answer:

1.16

Step-by-step explanation:

Given that;

For some positive value of Z, the probability that a standardized normal variable is between 0 and Z is 0.3770.

This implies that:

P(0<Z<z) = 0.3770

P(Z < z)-P(Z < 0) = 0.3770

P(Z < z) = 0.3770 + P(Z < 0)

From the standard normal tables , P(Z < 0)  =0.5

P(Z < z) = 0.3770 + 0.5

P(Z < z) =  0.877

SO to determine the value of z for which it is equal to 0.877, we look at the

table of standard normal distribution and locate the probability value of 0.8770. we advance to the  left until the first column is reached, we see that the value was 1.1.  similarly, we did the same in the  upward direction until the top row is reached, the value was 0.06.  The intersection of the row and column values gives the area to the two tail of z.   (i.e 1.1 + 0.06 =1.16)

therefore, P(Z ≤ 1.16 ) = 0.877

8 0
3 years ago
<img src="https://tex.z-dn.net/?f=%20%7B3%7D%5E%7B2%20%7D%20" id="TexFormula1" title=" {3}^{2 } " alt=" {3}^{2 } " align="absmid
expeople1 [14]

Answer: 9


Step-by-step explanation:

To square a number, you multiply it by itself twice.

In this case, your answer would be 3 x 3 = 9.

Hope it helps! :)

3 0
3 years ago
I need help please! ​
Sophie [7]

Answer/Step-by-step explanation:

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Area = 42 cm²

AD = (x + 8) cm

BC = (x + 5) cm

AB = x cm

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42 = ½((x + 8) + (x + 5))*x

42 = ½((x + 8 + x + 5)*x

42 = ½(2x + 13)*x

Multiply both sides by 2

42*2 = (2x + 13)*x

84 = 2x² + 13x

2x² + 13x = 84

Subtract both sides by 84

2x² + 13x - 84 = 0

4 0
3 years ago
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