QUADRATIC EQUATIONS : QUADRATIC EQUATIONS
DEFINITION : DEFINITION An equation of the form ax2+bx+c=0 is called a quadratic equation, where a, b, c are known values (i.e. constants), a is non-zero and x is the unknown value (i.e. a variable).
For example: 5x2+7x+3=0, 4x2+2=0, 3x2+8x+4=8, are all quadratic equations.
Slide 3 : Since the highest power of a quadratic equation is 2, a quadratic equation can have at the most two unique solutions (which are also called the roots of the equation). Thus, for a given quadratic equation, x can have at the most 2 unique values.
FORMULA : FORMULA
QUESTIONS : QUESTIONS How many roots has a quadratic?
2. What do we mean by a double root? .
ANSWERS : ANSWERS Always two.
The two roots are equal.
Example:
x^2- 10x + 25 = 0
(x-5)(x-5) = 0
If x=5 then each factor will be zero.
Here 5 is called the double root.
Solution by factoring : Solution by factoring Problem :
Find the roots of each quadratic by factoring.
a) x² - 3x + 2 = 0
Solution:
(x-1)(x-2) = 0
this implies either x=1 or x=2.
Notice that we use the conjunction "or," because x takes only one value at a time.
EXERCISE : EXERCISE 1. Solve X^2-11X+28 = 0
2. Solve X^2-13X = 68
3. Solve X(2X+5) = 7
4. Solve 9X^2+8 = 22X
5. Solve 4X^2 = 11X + 3
Use either factor method or formula method.
Solutions : Solutions X = (7,4)
X = (17,-4)
X = (1,-7/2)
X = (2,4/9)
X = (3,-1/4)
Slide 10 : THANK YOU