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A quadratic function will have a degree of two.
A quadratic inequality in x is in the standard form of ax^2+bx+c(>or<)d. Ex. 3x^2+5x+1>4
No. This is not an inequality, because you need something > something_else, or less than or 'not equal' or 'greater than or equal', etc. Since it has an x cubed term, it is not a quadratic.
In a linear inequality the variable is only present raised to the first power (which is usually not explicitly shown). In a quadratic the square of the variable is present (or implied). The square can be implied in an inequality such as x + 1/x < 6 (x not 0) This is equivalent to x2 - 6x + 1 < 0
The answer depends on the nature of the inequality: whether it is linear, quadratic or has some other functional form.