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Quadratic Equations, Quadratic Equations - Coggle Diagram
Quadratic Equations
Finding a solution set
ax²+bx+c=0
px.qx=ax²
m.n=c
pnx+qmx=bx
(
px+m).(qx+n)=0
x²+4x+3=0 → (x+3).(x+1) x=-3 x =-1
a≠0 a b c ∈ R,ax²+bx+c=0 is quadratic equation with the variable x
3x²+2x+5 is exaple of quadratic equation
3x³-4x+5 is not quadratic equation
The Concept of Discriminant
ax²+bx+c=0
b² - 4.a.c* is the formula
If Δ=b² - 4.a.c > 0
x1=-b+√¯Δ / 2a
x2=congujate
If Δ=b² - 4.a.c = 0
two roots are equal
-b / 2a
No real Roots
ax²+c=0
ax²=-c
x²= -c/a
-c/a > 0
Complex numbers
x²+9=0
x²=-9
x1=-√¯-9
x2=√¯-9
√¯-9 ∉ R
it shown as i and √¯-1
√¯-9)=3i
z1=5+3i
İmaginery part=3
Real part=5
Quadratic Equations
Forming a Quadratic Equation
If ax²+bx+c=0
x1+x2=b/a
x1.x2=c/a
