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QUADRATIC EQUATIONS, image, image, image, image - Coggle Diagram
QUADRATIC EQUATIONS
Definition
An equation containing a single variable of degree 2. Its general form is ax2 + bx + c = 0, where x is the variable and a, b, and c are constants (a ≠ 0).
The values of x that satisfy the equation are called solutions of the equation, roots or zeros of the expression on its left-hand side.
It has at most two solutions. If there is no real solution, there are two complex solutions.
Discriminant
In the quadratic formula, the expression underneath the square root sign is called the discriminant. b²-4ac.
If it is more than 0, the equation has two real solutions. If it's less than 0, there are no real solutions. If it's equal to 0, there is one real solution.
Complex Numbers
A number that can be expressed in the form a + bi, where a and b are real numbers, and i is a symbol called the imaginary unit, and satisfying the equation i2 = -1.
For a + bi, a is called the real part and b is called the imaginary part.
The two complex numbers a+bi and a-bi are called conjugates of each other and the conjugate of z=a+bi is denoted by z̅=a-bi.
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Finding Solution Set
Put all terms on one side of the equal sign, leaving zero on the other side. Set each factor equal to zero.
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