Polynomial vs. Quadratic — What's the Difference?
By Urooj Arif & Fiza Rafique — Updated on May 7, 2024
A polynomial is a mathematical expression involving sums of powers of variables, while a quadratic is a specific type of polynomial with a degree of 2.
Difference Between Polynomial and Quadratic
Table of Contents
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Key Differences
Polynomials are expressions comprising variables raised to various powers, combined using addition, subtraction, and multiplication. Quadratics are a specific subset of polynomials, always involving terms up to a power of two.
In polynomials, the highest power of the variable indicates the degree, determining the expression's behavior and shape. For quadratics, the degree is always 2, giving them a characteristic parabolic graph.
Polynomials can solve various equations, model relationships, or represent functions in different fields. Quadratic equations, with a specific form, often describe projectile motion, optimization problems, or geometric shapes like circles.
While polynomial equations can have multiple roots or solutions depending on their degree, quadratic equations always have up to two real or complex roots.
Comparison Chart
Definition
Expression involving sums of powers
Polynomial of degree 2
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Degree Range
Any degree (0, 1, 2, etc.)
Always degree 2
Graph Shape
Depends on degree
Parabola
Number of Roots
Up to degree number
Up to two
Compare with Definitions
Polynomial
An algebraic expression involving terms with variables raised to varying powers.
The polynomial 3x4 −2x2 +5 has a degree of 4.
Quadratic
A polynomial with the highest power of the variable being two.
A quadratic function like 2x2 +3x−4 forms a parabolic shape.
Polynomial
An algebraic function that forms a continuous, smooth curve.
Polynomial functions have continuous derivatives.
Quadratic
An equation that can have up to two real or complex roots.
The quadratic equation x2 −5x+6=0 has two real roots.
Polynomial
A function where the largest power of a variable is known as the degree.
A polynomial of degree 5 will have up to five roots.
Quadratic
An expression that can represent parabolic paths in physics or geometry.
The quadratic model accurately described the projectile's path.
Polynomial
An expression where terms include coefficients and non-negative integer exponents.
In the polynomial 2x3 −x+4, the coefficient of is 2.
Quadratic
An expression where the variable's highest power is two.
Solving quadratic equations can be done using the quadratic formula.
Polynomial
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. An example of a polynomial of a single indeterminate x is x2 − 4x + 7.
Quadratic
Of, relating to, or containing quantities of the second degree.
Polynomial
Of, relating to, or consisting of more than two names or terms.
Quadratic
Of or relating to the second power;
Quadratic equation
Polynomial
A taxonomic designation consisting of more than two terms.
Quadratic
Square-shaped
Polynomial
An algebraic expression consisting of one or more summed terms, each term consisting of a constant multiplier and one or more variables raised to nonnegative integral powers. For example, x2 - 5x + 6 and 2p3q + y are polynomials. Also called multinomial.
Quadratic
(mathematics) of a polynomial, involving the second power (square) of a variable but no higher powers, as . Category:en:Polynomials
Polynomial
An expression of two or more terms.
Quadratic
(mathematics) of an equation, of the form .
Polynomial
An expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power, such as . Category:en:Polynomials
Quadratic
(mathematics) of a function, of the form .
Polynomial
(taxonomy) A taxonomic designation (such as of a subspecies) consisting of more than two terms.
Quadratic
(mathematics) A quadratic polynomial, function or equation.
Polynomial
(algebra) Able to be described or limited by a polynomial.
Quadratic
Of or pertaining to a square, or to squares; resembling a quadrate, or square; square.
Polynomial
(taxonomy) of a polynomial name or entity
Quadratic
Tetragonal.
Polynomial
An expression composed of two or more terms, connected by the signs plus or minus; as, a2 - 2ab + b2.
Quadratic
Pertaining to terms of the second degree; as, a quadratic equation, in which the highest power of the unknown quantity is a square.
Polynomial
Containing many names or terms; multinominal; as, the polynomial theorem.
Quadratic
An equation in which the highest power of an unknown quantity is a square
Polynomial
Consisting of two or more words; having names consisting of two or more words; as, a polynomial name; polynomial nomenclature.
Quadratic
A polynomial of the second degree
Polynomial
A mathematical expression that is the sum of a number of terms
Quadratic
Of or relating to or resembling a square;
Quadratic shapes
Polynomial
Having the character of a polynomial;
A polynomial expression
Common Curiosities
How are polynomials classified by degree?
Polynomials are classified based on their highest degree term, like linear (1), quadratic (2), cubic (3), etc.
Can a polynomial have more than one variable?
Yes, multivariable polynomials involve multiple variables with different powers.
Do quadratic equations always have real roots?
No, quadratic equations can also have complex roots if their discriminant is negative.
Can a polynomial be linear?
Yes, if the highest degree of the polynomial is one, it is considered linear.
Are polynomials used outside of algebra?
Yes, polynomials model real-world phenomena in physics, engineering, economics, and other fields.
How many roots can a quadratic equation have?
Quadratic equations can have up to two real or complex roots.
How many terms can a polynomial have?
Polynomials can have any number of terms, from one to several, depending on their degree.
What is a polynomial in math?
A polynomial is a mathematical expression involving terms with variables raised to various powers.
Is a quadratic always a polynomial?
Yes, quadratics are a specific subset of polynomials.
What shapes do quadratic equations form?
Quadratic equations form parabolic shapes on a graph.
What is a quadratic function's vertex?
The vertex is the point where the quadratic function's parabola is at its maximum or minimum.
Can a polynomial have fractional powers?
No, polynomials only have non-negative integer powers.
What is the degree of a polynomial?
The degree is the highest power of the variable in the polynomial.
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Written by
Urooj ArifUrooj is a skilled content writer at Ask Difference, known for her exceptional ability to simplify complex topics into engaging and informative content. With a passion for research and a flair for clear, concise writing, she consistently delivers articles that resonate with our diverse audience.
Co-written by
Fiza RafiqueFiza Rafique is a skilled content writer at AskDifference.com, where she meticulously refines and enhances written pieces. Drawing from her vast editorial expertise, Fiza ensures clarity, accuracy, and precision in every article. Passionate about language, she continually seeks to elevate the quality of content for readers worldwide.
