Question

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Answer 1

Step-by-step explanation:

check ur answer....................

Answer 2

Since the eqaution have 6degree ,so it will have 6roots...

Let the roots be

y1,y2,y3,y4,y5,y6....

now,

sum of roots=-(coeeficient of x^5)/(coefficient of x^6)

so,

y1+y2+y3+y4+y5+y6=12

arithmetic mean of these roots are

(y1+y2+y3+y4+y5+y6)/6=12/6=2....i)

Hence arithmetic mean=2.......ii)

product of the roots=constant terms/1=64

y1×y2×y3×y4×y5×y6=64

geometric mean,of this will be eqaul to

y1×y2×y3×y4×y5×y6)^1/6=2

Hence ,

geometric mean=2......iii)

From the eqaution ii) and iii),we get

geometric mean=Arithmetic mean

This can only be possible if all the terms are same

Hence

y1=y2=y3=y4=y5=y6....iv)

putting this value in I)

we get

roots=2,2,2,2,2,2

if they are roots

Then by factor theorem

(x-2),(x-2),(x-2),(x-2),(x-2),(x-2)

will be the factors of the given polynomial f(x)

(x-2)^6=p(x)

p(x)=(x-2)^3(x-2)^3

p(x)={x^3-8-6x(x-2)}{x^3-8-6x(x-2)}

p(x)=(x^3-8-6x^2+12x)(x^3-8-6x^2+12x)

p(x)=x^6-12x^5+60x^4-160x^3+240x^2-192x

Now, comparing this with,f(x)

we can say,d is the greatest one

Hence optionC) is right