Question

Find all of the zeros of the function f(x) = 7x3 – 93x2 + 368x – 420.

Answer 1

`x=2,x=(30)/(7),x=7`

Explanation:

The given polynomial function is
`f(x)=7x^3-93x^2+368x-420`.

Using the intercept method, we graph the given polynomial function.

The x-intercepts of the graph represents the zeros of the given function.

From the attached graph, the function has zeros at:

`x=2,x=(30)/(7),x=7`

Answer 2

Answer:
`x=2,7,(30)/(7)`

Explanation:

Given

`7x^3-93x^2+368x-420=0`

Split the terms

`7x^3-14x^2-79x^2+158x+210x-420=0`

`7x^2\left ( x-2\right )-79x\left ( x-2\right )+210\left ( x-2\right )=0`

`\left ( x-2\right )\left ( 7x^2-79x+210\right )=0`

`\left ( x-2\right )\left ( 7x^2-49x-30x+210\right )=0`

`\left ( x-2\right )\left ( 7x\left ( x-7\right )-30\left ( x-7\right )\right )=0`

`\left ( x-2\right )\left ( x-7\right )\left ( 7x-30\right )=0`

therefore

`x=2,7,(30)/(7)`