Answer to Question #138851 in Calculus for Cassie Noel

Question

Decide whether or not the equation 2³-x²-3x+1=0 has a root between 1 and 2. Justify your answer.

Answer 1

We have function f(x)=2³-x²-3x+1=-x²-3x+9.

f(1)=-1-3+9=5>0,

f(2)=-4-6+9=-1<0.

It means that it should be a root between 1 and 2.