Given that `sqrt(3)` is a zero of a polynomial `6x^(3)+sqrt(2x^(2))-10x-4sqrt(2)`, find the other two zeroes.

Answer

N/a

Explanation

Let `" " p(x)=6x^(3)+sqrt(2)x^(2)-10x-4sqrt(2)`
`:' sqrt(2)` is a zero p(x).
`:. (x-sqrt(2))` is a factor of p(x).

`:. " " p(x)=6x^(3)+sqrt2)x^(2)-10x-4sqrt(2)`
`=(x-sqrt(2))(6x^(2)=7sqrt(2)x+4)`
`x(x-sqrt(2))(6x^(2)+4sqrt(2)x+3(sqrt2)x+4)`
`=(x-sqrt(2)){2x(3x+2sqrt(2))+sqrt(2)(3x+2sqrt(2))}`
`=(x-sqrt(2))(3x+2sqrt(2))(2x+sqrt(2))`
Now, `" " p(x)=0`
`implies (x-sqrt(2))(3x+2sqrt(2))(2x+sqrt(2))=0`
`implies " " x-sqrt(2)=0 " " or " "3x+2sqrt(2)=0 " " or " "2x+sqrt(2)=0`
`implies " " x=sqrt(2) " "or " "x=-(2sqrt(2))/(3)" " or " "x=-(sqrt(2))/(2)`
`:.` Other two roots are `(-2sqrt(2))/(3)` and `(-sqrt(2))/(2) " "` Ans.