Math, asked by saramaryam, 8 months ago

anyone knows the answer?​

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Answered by Mihir1001
14

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<font color="blue" size="5px"><b>Answer:</b></font>

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\huge\boxed{\fcolorbox{red}{#ffdfff}{q = 8}}

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<font color="red" size="5px"><b>Step-by-step-explaination:</b></font>

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let,

p(x) =  {x}^{2}  - 6x + q

let  \alpha and  \beta be the zeroes of the polynomial p(x).

let,

 \alpha  = 2 \beta

Now,

sum of zeroes =  \alpha  +  \beta

 \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  = 2 \beta  +  \beta

 \implies sum \: of \: zeroes = 3 \beta

 \implies  \frac{ - ( - 6)}{(1)}  = 3 \beta

 \implies 3 \beta  = 6

 \implies  \beta  = 2

Therefore,

 \alpha  = 2 \beta

 \implies  \alpha  = 2(2)

 \implies  \alpha  = 4

Now,

Product of zeroes =  \alpha  \beta

 \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  = (4)(2)

 \implies  \frac{q}{1}  = 8

 \implies q = 8

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Answered by devilakshmi16042004
0

Answer: 8

Step-by-step explanation:

Now let's assume that the two zeroes are a and 2a

Now the sum of the zeroes will be -b/a

And product of the zeroes will be c/a

a=1

b=-6

c=q

Now sum of the zeroes is a+2a = 6/1

3a = 6. So a = 2

Now the product of the zeroes is a×2a = q/1

2a^2 = q

2(2)^2 = q. (Coz a=2)

2×4=q

q=8

So answer is 8

Hope it's helpful

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