Quadratic Trinomial
A quadratic trinomial is a specific kind of mathematical expression containing both variables and constants. It appears in the form (ax2 + bx + c), where (x) is the variable, and (a), (b), and (c) are real numbers that are not zero. Here, (a) is called the leading coefficient, (b) is the linear coefficient, and (c) is the additive constant.
There’s a key aspect related to quadratic trinomials, called the discriminant (D), expressed as (D = b2 – 4ac). The discriminant helps categorize different cases of quadratic trinomials. By evaluating (D), you can understand more about the nature of the quadratic expression.
If a quadratic trinomial, which involves just one variable, equals zero, it transforms into what’s known as a quadratic equation, represented as (ax2 + bx + c = 0). In simpler terms, when a quadratic trinomial takes this form, it becomes a quadratic equation.
Must Read
Identities of Trinomials
Trinomial identities refer to formulas involving algebraic expressions with three terms.
- Factorization Identity: (a + b)(a + c)(b + c) = (a + b + c)(ab + ac + bc) − abc
- Square Sum Identity: a2 + b2 + c2 = (a + b + c)2 − 2(ab + ac + bc)
- Sum of Cubes Identity: a3 + b3 + c3 −3abc = (a+b+c)(a2 + b2 + c2 − ab − ac − bc)
Trinomials
A trinomial is a type of polynomial that consists of three terms. These terms are usually written as ax² + bx + c, where a, b, and c are constants, and x is the variable. Trinomials are common in algebra, particularly when dealing with quadratic equations, which can often be expressed or factored into trinomial form.
It is the expression that consist of three terms, the common form of trinomial is ax2 + bx + c. Trinomials in algebra, are essential for solving quadratic equations and analyzing various mathematical models.
Let’s know more about Trinomials definition, formula and examples in detail.