QUADRATIC EQUATIONS

NOTES :

1. The general form of a quadratic equation is ax^2 + bx + c = 0 , a, b, c are constants and a is not equal to 0.
2. Characteristics of a quadratic equation :

(a)     involves only ONE variable

(b)     has an equal sign “ = ” ,

         and can be expressed in the form ax^2 + bx + c = 0 

(c)     the highest power of the variable is 2

3. The roots of a Quadratic equation

(a)     “Root” refers to a specific value which satisfies the Q.E

(b)     Example : Given Quadratic equation x^2 + 2x - 3 = 0 

By substitution, it is found that :

         when x = 1 , then (1)^2 + 2(1)-3=0

          Hence, 1 is a root of the QE

But if     x=2, (2)^2+2(2)-3 not equal to 0, then 2 is NOT a root of the given QE

(c)     If the product of two numbers is zero, then either one or both the numbers must be zero .

If             xy = 0

Then      x = 0  or   y = 0

Or            x = y = 0 ( both are zeroes)

Example :                If             ( x – 2 ) ( x + 3 ) = 0

                                Then       x – 2 = 0     or     x + 3 = 0

                                                      x = 2    or           x = - 3  

                        ** 2 and -3 are called the roots of the equation ( x – 2 ) ( x + 3 ) = 0           

4. Methods that can be used to  solve QE

(a)     by Factorisation

(b)     by Completing the square

(c)     using formula       

TRY THE EXERCISE BELOW :

Challenge 1   Solve the quadratic equation  3x(x – 2) = 5 – x. Give your answer correct to three decimal places.   The answer is :   x = 2.370         or     x = – 0.703   Able to get it , well done. If not, please try again..

Challenge 2   Solve the quadratic equation  x 2 + 9x – 3 = 0 Give your answer correct to three decimal places.