Introduction
We took before :
The form of equation of first degree is ax+b=0
, The form of equation of second degree is ax²+bx+c=0
and the form of equation of third degree is ax³+bx²+cx+d=0
We call the equation by knowing the greatest power of the equation
The equation of second degree is called quadratic equation , we will have deep discussion about it at this lesson
Task
● At the end of the lesson the student should be able to :
- Deduce the methods of solving the quadratic equations
- Solve the examples about the lesson
- Feel the importance of the lesson in the daily life
● The student can use this link to show on the lesson https://youtu.be/wM9FsXJslec
●we will use this aids :
- Board
- Student book
- Coloured marker
Process
●The quadratic equation has 2 roots
●The methods of solving quadratic equations in one variable :
1- Solving quadratic equation in one variable algebraically :
○ By factorizing
by factorizing ax²+bx+c=0
To get the value of a,b " the roots of equation"
○ By the general law
by substituting in the general law to find the roots of the equation ax²+bx+c=0
the general law is : [- b +,- (b² - 4ac)½]/2a
Where, a: coefficient of x²
b: coefficient of x
c: absolute term
○Example : Find in R the solution set of :
1) x²-5x-6=0
2) 4x²=25
3) x²+6x+9=0
2- Solving quadratic equation in one variable graphically :
• Put the equation on the form ax²+bx+c=0
• Let f(x) = ax²+bx+c
• Graph the function f
• Determine the points of intersection of the curve with the x-axis , then the x- coordinates of these intersection points are the solution of the equation f(x) = 0
• We have 3 cases:
1) The curve intersect the x-axis at 2 points
2) The curve touches the x-axis at one point
3) The curve doesn't intersect the x-axis
Figures at page (12)
○Example : Find graphically the solution set in R :
1) x²-2x-3=0 , using the interval [-2,4]
2) -x² -4x -4=0 , using the interval [-5,1]
3) x²+2=0 , using the interval [-3,3]
○Remark : If we don't have interval , we will find the vertex point of the curve :
(-b/2a , f(-b/2a))
○Example : Find graphically the solution set of:
4x(x-1) -5 =0
then verify the result algebraically given that
( (6)½ = 24 )
Evaluation
● The evaluation will be done on the extent of interaction and cooperation in teamwork and solving problems on the lesson
| Degree | 1 | 3 | 5 | Final degree |
| Presentation | the presentation is random and doesn't serve the purpose | the presentation serve the purpose in simple way and need some arrangement | the presentation is organized and the tasks is distributed cooperatively | |
| Team work | work alone | organized work , not everyone was involved | organized work , the tasks are distributed interactively | |
| Solving examples | the example is not solved correctly | one example is solved ond onther is not | two examples are solved correctly | |
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Total degree : 25 , Final degree :
Conclusion
Quadratic equations in one variable take the form ax²+bx+c=0
We can solve the quadratic equation algebraically and graphically
Teacher Page
●Quadratic equation in one variable , page(9)
●methods of solving quadratic equation, page(10)
●Examples , page (12)