Question

I'm have problems solving this equations can someone please help me

Answer 1

Well, like many problems, I think it would be best to start with writing the information we already know. First, of all we know

• 
  `f(5) = 0`
• 
  `f(-2) = 70`
• 
  `f(x) = 6x^3 - 23x^2 + cx + 100`

Using this information, we can create the following equations:

• 
  `f(5) = 6(5)^3 - 23(5)^2 + 5x + 100 = 0`
• 
  `f(-2) = 6(-2)^3 - 23(-2)^2 - 2c + 100 = 70`

Simplifying, we get the following:

• 
  `275 + 5c = 0`
• 
  `-40 - 2c = 70`

Now, let's solve one of the equations for
`c`:

`275 + 5c = 0`

`275 = -5c`

`c = -55`

Now, we can substitute in 55 for
`c` to get the following:

`f(x) = 6x^3 - 23x^2 - 55x + 100`

Now we need to solve
`f(x)`. We already know that
`x = 5` is a zero of the equation, so let's divide our entire equation by
`(x - 5)` using synthetic division. This is a little hard to show here, but our result is:

`6x^2 + 7x - 20`

Now, we can solve by factoring:

`(3x - 4)(2x + 5) = 0`

`3x - 4 = 0`

`x = (4)/(3)`

`2x + 5 = 0`

`x = - (5)/(2)`

Our final zeros are
`\boxed{x = 5, (4)/(3), - (2)/(5)}`