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QUADRATIC EQUATIONS

 QUADRATIC EQUATIONS

Let's start with a videoa about Mohammed ibn-Musa Al-Kwarizmi 

A quadratic equation is an equation that can be written in the form
ax² + bx +c = 0 with a not equal to 0.

Quadratic equations can be complete ax²+bx+c=0 and incomplete ax²=0, ax²+bx=0, ax²+c=0 

The next video will show you how to solve  complete quadratic equations: 

 

Let’s see know how to solve incomplete quadratic equations:


ax²+bx+c=0 is called incomplete, if either b=0 or c=0 or both equals 0.


There are three kinds of incomplete quadratic equations:

  1. ax²+bx=0

To solve this kind of equations you should follow the following steps:

ax²+bx=0 ⇒ x(ax+b)=0 ⇒ x=0 

                                    ⇒ ax+b=0 ⇒ x= -b/a


Example:


2x²+8x=0 ⇒2x(x+4)=0 ⇒2x=0 ⇒x=0


                                    ⇒x+4=0 ⇒ x=-4

2. ax²+c=0

  To solve this kind of equation you should find the value of x:

ax²+c=0 ax²=-c x²=-c/a x=±√(-c/a)


Example:


x²-25=0 x²=25 x=±√25 x=±5


x²+25=0 x²=-25 x=±√(-25) No real solution.


 3. ax²=0

   This kind of equation has only one solution: x=0

 

 

 

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