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QUADRATIC EQUATIONS - Coggle Diagram
QUADRATIC EQUATIONS
What Are Discrimants?
We call the term b2 −4ac the discriminant.
It is symbolised by delta
What are Quadraric Equations?
, the expressions in the form of ax square +bx square+ c=0 are called quatratic equations
a,b and c are called coeffitents
The values of x which satisfy the given equation are called the
the solution of the equation
A quadratic equation has at most two solutions
If there is no real solution, there are two complex solutions
f there is only one solution, one says that it is a double root.
A quadratic equation always has two roots, if complex roots are included and a double root is counted for two
Complex Numbers
The imaginary number “i” is defined as the number whose square is -1.(square root of -1=i)
If we state For
a, b, c € R and a not equal to 0
Complex numbers are the numbers that have a real and an imaginary part.For example 8-2i.
They are defined by z
The two complex numbers a+bi and a-bi are called conjugates of
each other
Finding The Roots of A Quadratic Equation
.Roots are also called x-intercepts or zeros.
f (x) = ax2 + bx + c
The roots of the quadratic equation is given by this-->
A quadratic function can have one real root, two real roots, or no real roots.
If the discriminant is greater than zero, that function has two real roots
If the discriminant is less than zero, that function has no real roots
f(x) = x2 − 3x + 4.
b2 −4ac = (−3)2− 4 · 1 · 4 = 9 − 16 = −7.
If the discriminant is equal to zero, that function has exactly one real root
f(x) = −4x2 + 12x − 9.
b2 −4ac = (12)2− 4 · −4 · −9 = 144 − 144 = 0.
