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.
⇒ [tex]f(x) = x^3- 5x^2 + 6x[/tex]
⇒ [tex]f(0) = 0^3- 5(0)^2 + 6(0)[/tex]
⇒ [tex]f(0) =0[/tex]
At x = 2 .
From the graph , at x=2 we have f(x) = 0 i.e.
⇒ [tex]f(x) = x^3- 5x^2 + 6x[/tex]
⇒ [tex]f(0) = 2^3- 5(2)^2 + 6(2)[/tex]
⇒ [tex]f(0) =0[/tex]
At x=3 .
From the graph , at x=3 we have f(x) = 0 i.e.
⇒ [tex]f(x) = x^3- 5x^2 + 6x[/tex]
⇒ [tex]f(0) = 3^3- 5(3)^2 + 6(3)[/tex]
⇒ [tex]f(0) =0[/tex]
Therefore , the solutions to the related equation are 0,2,3 .
