Obtian all other zeroes of `(x^(4)+4x^(3)-2x^(2)-20x-15)` if two of its zeroes are ` :' sqrt(5)` and `-sqrt(5)` .

Answer

N/a

Explanation

Let `" " P(x)=x^(4)+4x^(3)-2x^(2)-20x-15`
`:. x-sqrt(5)` and `x-sqrt(5)` are factors of p(x). So. `(x-sqrt(5))(x+sqrt(5))=x^(2)-5` is a factor of P(x).

`:. " "p(x)=x^(4)+4x^(3)-2x^(2)-20x-15=(x^(2)-5)(x^(2)+4x+3)`
`=(x^(2)-5)[x^(2)+x+3x+3]=(x^(2)-5)[x(x+1)+3(x+1)]`
`=(x^(2)-5)(x+1)(x+3)`
`:. ` The other zeroes are given by
`x+1=0 " " or " " x+3=0`
`implies " " x=-1 " " or " "x=-3`
Hence, other zeroes are -1 and -3. `" "` Ans.