How do i solve `f(x)= x^3 +x^2 +x -2`  ?  I've tried factorising but im stuck. They want my answer to be in an intervall of length 1/4

Expert Answers

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`f(x)= x^2 + x^2 +x -2`

We will use the substitution to find the approximate root.

From the graph below, we notice that the root is between 0 and 1.

==> x=0 ==> f(0)= -2

==> x= 1==> f(1)= 1

Then the root between 0 and 1

We will try x= 1/2

==> x= 1/2 ==> f(1/2)= -1.125

Now we know that the root between 1/2 and 1.

We will try 3/4

==> f(3/4)= -0.265625

Then, we notice that the root is located between 3/4 and 1.

Then, `x in (3/4, 1)`

 

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