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

Question

asked Feb 16, 2022 195k views

1 Answer

Jagrati Modi · Answer 1 · 2022-02-21T23:00:33+0000

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
and
.