Question

Hello! I need some help with this homework question, please? The question is posted in the image below. Q6

Answer 1

Step 1

Given;

`g(x)=3x^2-5x-2`

Required; To find the zeroes by factoring

Step 2

Find two factors that when added gives -5x and when multiplied give -6x

`\begin{gathered} \text{These factors are;} \\ -6x\text{ and x} \end{gathered}`
`\begin{gathered} -6x* x=-6x^2 \\ -6x+x=-5x \end{gathered}`

Factoring we have and replacing -5x with -6x and x we have

`\begin{gathered} 3x^2-6x+x-2=0 \\ (3x^2-6x)+(x-2)_{}=0 \\ 3x(x-2)+1(x-2)=0 \\ (3x+1)(x-2)=0 \\ 3x+1=0\text{ or x-2=0} \\ x=-(1)/(3),2 \\ \text{The z}eroes\text{ are, x=-}(1)/(3),2 \end{gathered}`

Graphically the x-intercepts are;

The x-intercepts are;-1/3,2

Hence, the answer is the zeroes and x-intercepts are the same, they are;

`-(1)/(3),2`