Iteration

The equation  has a solution between  and .

Use a suitable method to find this solution correct to two decimal places.

A value of  between 2 and 3 satisfies the equation

By writing the equation in the form  where  and  are integers you should find, determine the value of correct to one decimal place.

Student A decides to solve the equation using the quadratic formula and gets the two solutions
 

Student B decides to solve the equation using a sign-change method between and , where  is an integer.
They want to find the larger solution to 1 decimal place.

Show Student B's working, stating clearly the value of .

The volume of a sphere of radius  cm, where , is 5 cm³ more than the volume of a square-based cuboid with height 10 cm, width cm and length cm.

Use a suitable method to find  to 1 decimal place.

[In this question, you may use that the volume of a sphere of radius is ]

The equation  has a solution between  and .

Find this solution correct to 1 decimal place.
Show your working.
 

x = .......................................................

It is known that the equation    has a solution that lies between and .

Use a suitable method to find the solution correct to 1 decimal place.
You must show your working clearly.
 

x = .......................................................

The equation  has a negative solution and a positive solution.
The positive solution lies between and .

Use a suitable method to find the positive solution correct to 1 decimal place.
Show your working.
 

t = .......................................................

Show that the equation has a solution between  and .