Question

One zero of the polynomial 3x^3+16x^2+15x-18 is 2/3 find the other zero of the polynomial

Answer 1

Answer:

The other zero of the polynomial is 3.

Step-by-step explanation:

The given polynomial is

$P(x)=3x^3+16x^2+15x-18$

$P(x)=x^3+16x^2+15x-18$

It is given that 2/3 is the zero of the given function. It means $(x-\frac{2}{3})$ is the factor of the given polynomial.

Use long division method to find the remaining factors.

$P(x)=(x-\frac{2}{3})(3x^2+18x+27)$

$P(x)=3(x-\frac{2}{3})(x^2+6x+9)$

$P(x)=3(x-\frac{2}{3})(x+3)^2$

Equate P(x)=0, to find the remaining zeros.

$x-\frac{2}{3}=0\Rightarrow x=\frac{2}{3}$

$(x+3)^2=0\Rightarrow x=-3$

Therefore the other zero of the polynomial is 3.