Question

If -1 is one of the zeroes of py 3x^3-5x^2-11x-3 find other zeroes

Answer 1

Given:

The function is:

`y=3x^3-5x^2-11x-3`

It is given that -1 is a zero of the given function.

To find:

The other zeroes of the given function.

Solution:

If c is a zero of a polynomial P(x), then (x-c) is a factor of the polynomial.

It is given that -1 is a zero of the given function. So,
`(x+1)` is a factor of the given function.

We have,

`y=3x^3-5x^2-11x-3`

Split the middle terms in such a way so that we get (x+1) as a factor.

`y=3x^3+3x^2-8x^2-8x-3x-3`

`y=3x^2(x+1)-8x(x+1)-3(x+1)`

`y=(x+1)(3x^2-8x-3)`

Again splitting the middle term, we get

`y=(x+1)(3x^2-9x+x-3)`

`y=(x+1)(3x(x-3)+1(x-3))`

`y=(x+1)(3x+1)(x-3)`

For zeroes,
`y=0`.

`(x+1)(3x+1)(x-3)=0`

`(x+1)=0` and
`3x+1=0` and
`x-3=0`

`x=-1` and
`x=-(1)/(3)` and
`x=3`

Therefore, the other two zeroes of the given function are
`-(1)/(3)` and
`3`.