IsQuadratic

IsQuadratic[ expr, x ] checks if an expression is quadratic in a variable, and returns its coefficients.

Usages

`IsQuadratic[ expr, x ]`

IsQuadratic[ expr, x ] checks whether expr can be written as a x^2 + b x + c with a ≠ 0, where a, b and c do not depend on x. Brackets are expanded first. If so, the result is IsQuadraticResult[a=>a, b=>b, c=>c]; otherwise the result is False. In a script, wrap the command in Simplify.

Example	in	out
A quadratic expression.	`Simplify[ IsQuadratic[2x^2 + 3x + 1, x] ]`	`IsQuadraticResult[a=>2, b=>3, c=>1]`
Brackets are expanded.	`Simplify[ IsQuadratic[(x + 1)^2, x] ]`	`IsQuadraticResult[a=>1, b=>2, c=>1]`
A product.	`Simplify[ IsQuadratic[x(x - 3), x] ]`	`IsQuadraticResult[a=>1, b=>-3, c=>0]`
Other variables are allowed in the coefficients.	`Simplify[ IsQuadratic[x^2 + y, x] ]`	`IsQuadraticResult[a=>1, b=>0, c=>y]`
A linear expression is not quadratic.	`Simplify[ IsQuadratic[3x + 1, x] ]`	`False`
A cubic expression is not quadratic.	`Simplify[ IsQuadratic[x^3 + x, x] ]`	`False`

Using the result

Use Type to check the result, and GetOption to get the coefficients.

Example	in	out
Get the coefficients.	`r := Simplify[IsQuadratic[2x^2 + 3x + 1, x]] a := GetOption[r, 'a'] b := GetOption[r, 'b'] c := GetOption[r, 'c']`	`a = 2` `b = 3` `c = 1`
Check whether the expression is quadratic.	`r := Simplify[IsQuadratic[x + 1, x]] If[Type[r] == IsQuadraticResult] t := 1 Else t := 0 End`	`t = 0`

Details

Without Simplify, the command is not calculated.

Warning

Do not check the result with r == False: for a quadratic expression this comparison cannot be decided, so in an If it is treated as True. Use Type[r] == IsQuadraticResult, as in the example above.

See also: IsLinear, PolynomialDegree, Solve, Type