mathematics
  Personalized »

KS3
 
 
 
Year 7
 
 
Year 8
 
 
Year 9

KS4
 
 
 
Year 10
 
 
Year 11

A-levels
 
 
 
Year 12 (AS)
 
 
Year 13 (A-levels)


physics
  Personalized »

 
 


KS4
 
 
 
KS4 Level Physics

A-levels
 
 
 
AS Level Physics
 
 
A-levels Physics


 
 
Private tutors
 
 
Find a tutor »


 


Unlock access to content
 
Select one option:



Free of charge
Unlock the chapter   "Zeros of polynomials"  



Unlock access to the solution of problems in this chapter.
Free of charge Price: 5 £

Continue »
Subscribe to OpenProf     If you do not get a better grade, you get your money back!
 


Unlock access to all problems solutions.
Available from 10.75 £ / month.
Continue »
mathematics UK Year 13 Mathematics (A Levels)
 
Solved problems for the chapter:
 

Zeros of polynomials

download pdf
View the theory »
The secant method for finding roots
open
View the theory »
Solving linear equations and systems of equations for KS4
open
View the theory »
Zeros of a polynomial for AS level
open
View the theory »
Polynomial for KS4
open
↓   Show theory [4]   ↓


Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:zeros_of_polynomials/5566/


Example 1.
Write a polynomial:

third degree with zeros at - 1, 2, 3 and has a value of 4 at point 1.

    
Example 2.
Using the secant method, find the real zero of the given polynomial to the nearest hundredth:

    
3.
Using the secant method, find the real zero of the given polynomial to the nearest hundredth:

    
4.

Write an equation whose solutions are 0, 1 and -5.

    
5.
Using the secant method, find the real zero of the given polynomial to the nearest hundredth:

    
6.

Solve the inequality:


    
7.
Using the secant method, find the real zero of the given polynomial to the nearest hundredth:

    
8.

Solve the equation:


    

9.
Using the secant method, find the real zero of the given polynomial to the nearest hundredth:

    
10.

Write equation whose solutions are 0, 7 and -7 .

    
11.

Simplify each of the equation below Abs write out the exact solution:









    
12.
Prove:

that given values of x are zeros of the polynomial:




  • 2

  • 2i

  • -1

  • 1

    
13.

Find all the solutions to the equation:


    
14.

Write the equation whose solutions are , and .

    
15.
Prove:

that the given values are zeros of the polynomial :







    
16.

Find all the solutions to the equation:


    
17.

Determine the degree, the leading coefficient and the constant term for the given polynomial:


    
18.
List the zeros of the polynomial:

    

19.

Find all the solutions to the equation:


    
20.
List the zeros of the polynomial:

    
21.
Determine the degree, the leading coefficient and the constant term for the given polynomial:

    
22.
List the zeros of the polynomial:

    
23.

Write the equation whose solutions are , and .

    
24.
List the zeros of the polynomial:

    
25.
Determine the degree, the leading coefficient and the constant term for the given polynomial:

    
26.
List the zeros of the polynomial:

    
27.
Determine the degree, the leading coefficient and the constant term for the given polynomial:

    
28.
List the zeros of the polynomial:

    

29.
Determine the degree, the leading coefficient and the constant term for the given polynomial:

    
30.
   
31.

Given the polynomial




Identify and write down:

  • the degree of the polynomial,

  • the constant term of the polynomial,

  • the leading coefficient of the polynomial,

  • .

    
32.
Write a polynomial:

fourth degree having double zero at -1 and single zero at 2, 3, and at point -2 a value of 10.

    
33.

Determine the degree, leading term and constant term of the polynomial below:


    
34.
Write a polynomial:

third degree with zeros at - 2,2,3 and has a value of 12 at point 1.

    
35.

Given the polynomial:




  • For and , calculate the zeros of the polynomial. Determine the domain of the function .


  • Compute and if one of the zeros of the polynomial p is .


  • Calculate and if the tangent to the graph of the polynomial p at the point is parallel to the line .

    
36.
Write a polynomial:

A fourth degree polynomial that has a double zero at - 3 and a second double zero at 1 and has a value of - 9 at point - 2.

    
37.

Calculate the zeros of the polynomial


    
38.
Write a polynomial:

third stage, which has zeros in and in - 1 and has in 1 value 6.

    

39.

Solve the equation:


    
40.

The polynomial below is given:




determine the unknowns a and b if it has zero at and is considered to be .

    
41.

Solve the equation:


    
42.

Check that the number is a double zero of the polynomial . Find the remaining two (complex) zeros.

    
43.

Calculate the zeros of the polynomial:


    
44.
Find unknowns a, b and c to which the following applies:

    
45.
Find the intervals for which the given polynomial has positive or negative values:

    
46.

Find the zeros of the function:




and sketch its graph.

    
47.

Given the polynomial




  • Determine the degree of the polynomial.

  • Find its zeros.

  • Find the initial value.

  • State the domain and the range.

  • Draw the polynomial graph.

    
48.

Given two polynomials:






  • Divide the polynomial p(x) by the polynomial q(x) and write the quotient and remainder.

  • Calculate the common zero of the two polynomials.

  • Calculate the value of the expression .

    

49.

Find the unknown polynomial if you know the following information about it:

  • is a fourth degree polynomial,

  • one of its zeros is equal to ,

  • the leading coefficient of the polynomial is equal to ,

  • At point , the graph touches the abscissa axis.


    
50.

Given a polynomial:




  • Calculate the zeros of the polynomial and the intersection of the polynomial with the y- axis.

  • Draw the graph of the polynomial in the given coordinate system.

  • Calculate the values of x for which the polynomial intersect the line .