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 $x=-\dfrac{1}{3}$ and $x=3$

Therefore, the other two zeroes of the given function are $-\dfrac{1}{3}$ and $3$.