Polynomials

mpx

drawing

Find the value of

.
2. In this question you must show detailed reasoning.

The diagram shows a sketch of the curve

, where

.

Find the values of

and

.
3. In this question you must show detailed reasoning.
(a) Show that

is a factor of

.
(b) Solve the equation

.
4. In this question you must show detailed reasoning.

Show algebraically that

is the only real root of the equation

.
5. In this question you must show detailed reasoning.
(a) Show that

is a root of the equation

.
(b) Solve the equation

.

Hence solve the equation

.
6. The polynomial

is defined by

.
(a)

and

are factors of

. Find the values of

and

.
(b) Factorise

completely.

Sketch the graph of

.
7. In this question you must show detailed reasoning.
(a) Sketch the curve

.
(b) Draw the line

on your graph.

Verify that the line and the curve intersect at the point

.
(d) Show that the

-coordinates of the points where the line and the curve intersect satisfy the equation

.
(e) Find the

-coordinates of the other two points of intersection of the line and the curve, giving your answers to two decimal places.

drawing