Quadretic Equations
Solutions of Quadretic Equations
Solution of a quadretic equation by completing the square
Solution of a quadretic equation by quasratic formula
Solution of a quadratic equation by factoring
Ex: 
Ex:
Complex Numbers
If Δ=b2- 4ac=0, there are rwo equal real roots such that x1=x2=b/2a
If Δ=b2- 4ac<0, there is no real root and the solution set is empty on R SS=∅
If Δ=b2- 4ac>0, there are two distinct real roots such that x1=-b+√¯Δ / 2a, x2= -b - √¯Δ / 2a.
The imaginary unit is i is deifned by i=√¯-1 or i2=-1 and the number set containing this is called complex number set. This set is denoted by C.
For z=a+bi; a is the real part of z, b is the imaginary of z
İmaginary Unit
Note: The number √¯-1=i is said the unit of imaginary number. Then, divide the power of "i" by 4 then look at remainder.
Conjugate of a Complex Number
The two complex numbers a+bi and a-bi are called conjugates of each other and the conjugate of x=a+bi is denoted by x̄=a-bi
Note: If a quadratic equation with real coefficients has a negative discriminant, the two solutions of the equation are complex conjugates of each other.
Ex: x2+2x+2=0 SS={(-1+1),(-1-1)}
The Relation Between the Roots and the Coefficients of a Quadratic Equations
x1.x2=c/a
x1+x2=-b/a
Forming a Quadratic Equation When the Roots are Given
S(sum)=x1+x2 and P(product)=x1.x2 are found. Then, it is written x2-Sx+P=0.