Question

Find the cubic polynomial with the sum of zeroes, sum of product of zeroes taken two at a time and product of its zeros as 1/√2, √3 and 1/√6.

I swear that your answer will be marked as brainliest.

Answer 1

Step-by-step explanation:

I hope you got it. Thank you

Answer 2

Answer:

√6x³-√3x²+3√2x-1

Step-by-step explanation:

let, sum of the zeroes= 1/√2

product of it's zeroes taken two at a time=√3

and

product of it's zeroes=1/√6

We have,

p(x)= k[x³-(sum of the zeroes)x²+(product of it's zeroes taken two at a time)x-(product of it's zeroes)]

put the values

p(x)= k[x³-(1/√2)x²+(√3)x-(1/√6)]

= k[x³-x²/√2+√3x-1/√6]

let k=√6

p(x)= √6[x³-x²/√2+√3x-1/√6]

= √6x³-√3x²+√18x-1

= √6x³-√3x²+(√9)(√2)x-1

= √6x³-√3x²+3√2x-1

{note: sum of the zeroes= alpha+beta+gama

product of it's zeroes taken two at a time= (alpha)(beta)+(beta)(gama)+(alpha)(gama)

and

product of it's zeroes= (alpha)(beta)(gama)}

hope it helps you dear