Question

Show that the function has a at least one real zero between x=1 and x=2

Answer 1

we have the function

`f(x)=7x^5-9x^4-x^2`

Simplify the expression

`f(x)=x^2(7x^3-9x^2-1)`

Find out the value of f(x) at x=1

For x=1

`\begin{gathered} f(x)=7(1)^5-9(1)^4-(1)^2 \\ f(x)=7-9-1 \\ f(x)=-3 \end{gathered}`

Find out the value of f(x) at x=2

For x=2

`\begin{gathered} f(x)=7(2)^5-9(2)^4-(2)^2 \\ f(x)=224-144-4 \\ f(x)=76 \end{gathered}`

Note that

For x=1 --------> f(x) is negative

For x=2 ------> f(x) is positive

that means

between the interval (1,2) the graph cross the x-axis

that means

The given function has at least one real zeros between x=1 and x=2