FACTORISATION

Quadratic expression and Equation

 

Question 1

The solution of the equation x² – 2x = 8 is  (UME 1979, Question 12)

 

Solution

 

Question 2

Find the roots of the equation  (UME 1980 Question 8)

 

Solution

                   

Question 3

The sum of the roots of a quadratic equation is  and the product of its roots is 4. The                            quadratic equation is (UME 1980, Question 47)

 

Solution

Quadratic equation is of the form                                    

Question 4

The solution of the quadratic  is given by  (UME 1982, Question 7)

 

Solution

                

                                      

               Question 5

The factors of  are (UME 1982, Question 6)

 

 

 

 

 

 

 

Solution

 

Question 6

The quadratic equation whose roots are  (UME 1984, Question 33)

Solution

The quadratic equation will be of the form

 

Question 7

Find the values of p for which the equation  has equal roots (UME                 1985, Question 13)

 

Solution

              

 

Question 8

If the quadratic function  is a perfect square, Find R (UME 1985 Question 21)                   Solution

 

 

Question 9

Solve the equation  (UME 1986, Question 21)

 

Solution

              

                Question 10

The minimum value of y in the equation  is (UME 1987, Question 28)

 

                Solution

 

Question 11

The solution of the quadratic equation  (UME 1988, Question 22)

 

Solution

                      

 

Question 12

For what value of Q will make the expression  a complete square (UME 1989,                 Question 24)

Solution

Question 13

What must be added to make  to make it a perfect square (UME 1990, Question 20)

 

Solution

              

 

Question 14

Find the solution of the equation  (UME 1990, Question 21)

Solution

 

Question 15

Solve the equation  (UME 1991, Question 23)

 

Solution

 

Question 16

At what value of x is the function  minimum?

Solution

             

            

 

                 Question 17

                  Solve the equation  (UME 1992, Question 12)                                  

 

                  Solution

                            

 

                   Question 18

                    Solve the equation  (UME 1993, Question 15)

                Solution

                  

                 

                  Question 19

                   (UME 1993, Question 10)

 

                   Solution

  

  

           

Question 20

Solve the equation  (UME 1998, Question 12)

Solution

              

                 Question 21

                 Find the minimum value of  for all real values of x (UME 1997, Question 13)

 

                 Solution

               

                    

               Question 22

               What value of g will make the expression 4x² – 18xy + g perfect square. (UME 1987                   

                Question 15)

           

              Solution

                                   

                       

 

                  Question 23

                   Find the range of value m for which the roots of the equation  

                    are real (UME 1998, Question 13)

 

                   Solution

                  

	+	+	+
	+	+	–
	+	+	–

 

 

 

 

 

                       The range of value is value

 

                Question 24.

                If a  are the roots of the equation  Find the value of

               (UME 2000, Question 22).

              Solution

                                      

 

        Question 25

       The minimum point on the curve  is at (UME 1978, Question 22)

 

       Solution

      

 

     Question 26

    

 

     Solution

        

2x – 5	+	–	+
x  + 7	+	+	+
(2x – 5) (x  + 7)	+	–	+

      The range is 

    

     Question 27

     Find the values of m which makes the following quadratic function a perfect square

      (UME 1986, Question 21)

 

     Solution

 

Question 28

 

 

 

 

 

 

       Which of the following equations represents the graph above?

       

             (UME 2009 Question 14, SetU03)

 

     Solution

     The root of the equation are – 2  and ¼ , This represent the zeroes of the equation, therefore the       

      original equation will be

The function of the equation will be y = 2 +7x – 4x²  

Answer: Option C