If 1 and -1 are zeroes of the polynomial `x^(3)+5x^(2)-x-5`, then find all zeroes of the given polynomial.

Answer

N/a

Explanation

Let `" " p(x)=x^(3)+5x^(2)-x-5`
`:' ` 1 and -1 are zeroes of p(x).
`:. ` x-1 and x+1 are factors of P(x).
`implies (x-1)(x+1)=x^(2)-1` is a factor of p(x).
On dividing p(x) by `x^(2)-1`,

`:. " " p(x)=x^(3)+5x^(2)-x-5=(x^(2)-1)(x+5)=(x-1)(x+1)(x+5)`
Now, `" "` p(x)=0
`implies (x-1)(x+1)(x+5)=0`
`implies " " x-1=0 " " or " "x+1=0 " " or " " x+5=0`
`implies " " x=1 " " or " " x=-1 or x=-5`
`:.` Zeroes of p(x) are 1, -1 and -5. `" "` Ans.