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QUADRATIC EQUATIONS
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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:
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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