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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:

- ax²+bx=0

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

- Move all terms to the same side, so the equation is set equal to 0.
- Factor the algebraic expression.
- Set each factor equal to 0. (If the product of two factors equals 0, then either one or both of the factors must be 0).
- Solve each resulting equation.

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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