Question

Graph the function f(x) = x3 – 5x2 + 6x using the graphing calculator. What are the solutions to the related equation? Check all that apply.
–3
–2
–1
0
1
2
3

Answer 1

the solutions to the related equation are 0,2,3 .

Step-by-step explanation:

Here we have , function  f(x) = x3 – 5x2 + 6x . Graph of this function is given below  . We need to find What are the solutions to the related equation . Let's find out:

Solution of graph means the  value of x at which the value of f(x) or function is zero . We can determine this by seeing the graph as at what value of x does the graph intersect or cut x-axis !

At x = 0 .

From the graph , at x=0 we have f(x) = 0 i.e.

⇒ $f(x) = x^3- 5x^2 + 6x$

⇒ $f(0) = 0^3- 5(0)^2 + 6(0)$

⇒ $f(0) =0$

At x = 2 .

From the graph , at x=2 we have f(x) = 0 i.e.

⇒ $f(x) = x^3- 5x^2 + 6x$

⇒ $f(0) = 2^3- 5(2)^2 + 6(2)$

⇒ $f(0) =0$

At x=3 .

From the graph , at x=3 we have f(x) = 0 i.e.

⇒ $f(x) = x^3- 5x^2 + 6x$

⇒ $f(0) = 3^3- 5(3)^2 + 6(3)$

⇒ $f(0) =0$

Therefore , the solutions to the related equation are 0,2,3 .