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QUADRATIC EQUATION. BERK TÜZEMEN 9/D 223. HISTORY OF ALGEBRA. Al-Khwarizmi was born around 780 in Baghdad and died there in or around 850. He was born in the epicenter of an Islamic empire which then stretched from the Mediterranean to India.

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quadratic equation

QUADRATIC EQUATION

BERK TÜZEMEN

9/D 223

history of algebra
HISTORY OF ALGEBRA
  • Al-Khwarizmi was born around 780 in Baghdad and died there in or around 850. He was born in the epicenter of an Islamic empire which then stretched from the Mediterranean to India.
slide3

. Al-Khwarizmi was one of the learned men who worked in the House of Wisdom. His interests lied in the fields of algebra, geometry, astronomy and geography. His now most famous work is that from which we got the name for algebra itself - Hisab al-jabrw'al-muqabala .

questions
QUESTIONS:

Solve the equation x²+x-12=0

Factorising, (x-3) (x+4) =0

Either x-3=0 or x+4=0

x=3 x=-4

Example 2:

Solve the equation 6x²+x-2=0

Factorising, (2x-1) (3x+2)=0

Either 2x-1=0 or 3x+2=0

2x=1 3x=-2

X=1/2 x=-2/3

solution by formula
Solution by formula:
  • The solutions of the quadratic equation ax²+bx+c=0 are given by the formula
example
Example:
  • Solve the equation 2x²-3x-4=0

In this case a=2, b=-3, c=-4

x=3+6.403÷4 x=3-6.403÷4x=2.35 x=-0.85

elimination and substitution
Elimination and Substitution:
  • Example:

Solve the following simultaneous equations:

2x+3y=7

3x+5y=11

slide8

By elimination:

3(2x+3y=7) 6x+9y=21 =a

2(3x+5y=11) 6x+10y=22 =b

b-a = y y=22-21y=1

2x+3(1)=7 2x=4 x=2

slide9

By substitution:

2x+3y=7

x=

3()+5y=11

y=22-21

y=1

slide10
ÖSS
  • Example:

x²+2x+a and a>5 . What is theinterval of a ? (1998-ÖYS)

solution
Solution:
  • x²+2x+a -5<0 forthis, it must be equalto0

=b2-4ac

=22-4.1(a-5)<0

=4-4a+20<0

=24<4a

=6<a

=6<a<∞