A rational function $\dfrac{P(x)}{Q(x)}$ is called proper when
Adegree of $P(x)$ is less than degree of $Q(x)$
Bdegree of $P(x)$ equals degree of $Q(x)$
Cdegree of $P(x)$ is greater than degree of $Q(x)$
D$Q(x)$ is a constant polynomial
Answer & Solution
Correct answer: A. degree of $P(x)$ is less than degree of $Q(x)$
1. By definition a proper rational function has numerator degree below denominator degree.
2. If not, it is improper and is first reduced by long division.
3. Hence option A is correct.
_Source: NCERT Class 12 Mathematics Ch 7 "Integrals", p.315_
Related questions
A rule counting sign changes to bound the number of positive real zeros belongs to:A single point where a rational graph is undefined, shown by an open circle, is a hole or A horizontal line that a graph approaches as inputs grow without bound is a horizontal:A vertical line that a graph rushes towards but never crosses is a vertical:A polynomial with real coefficients has 2 plus 3i as a zero, so it must also have as a zerFor a rational zero, numerators come from factors of the constant term and denominators frA polynomial takes a negative value at 3 and a positive value at 4, so between them it musA graph crosses straight through the x-axis at a zero. That zero has multiplicity that is: