Mathematics
Linear polynomials
रैखिक बहुपद
In this Class 9 Mathematics topic from “Introduction to Polynomials,” students learn how to recognize and work with linear polynomials, whose degree is one and which are commonly written as ax + b, where a is non-zero. They identify the variable, coefficient, constant term, and degree, distinguish linear polynomials from other types, evaluate them for given values, and understand how to find their zero. These ideas build a foundation for simplifying expressions and studying polynomial relationships.
Practice questions
If (p(x)=5-3x), which is (p(2x))?HardLevel 33A student says that \(5x-2+\frac{3}{x}\) is a linear polynomial because the highest power of \(x\) is 1. What is the student's error?HardLevel 33If (p(x)=kx+4) and (p(2)=p(-2)), when will (p(x)) remain linear?HardLevel 33If \(p(x)=ax+b\), where \(a\ne0\), is a linear polynomial, which statement about its zeroes is correct?HardLevel 33If (p(x)=2x+3) and (q(x)=5x-1), what is the degree of (q(x)-2p(x))?HardLevel 33Which option has zero \(\frac{11}{5}\) for a linear polynomial?HardLevel 33If (p(x)=3x-8), what is (p(x+1)-p(x))?HardLevel 33If (p(x)=\lambda x+6) and its zero is greater than (-2), which condition is correct when (\lambda>0)?HardLevel 33If \(p(x)=ax+b\), where \(a\ne0\), is a linear polynomial, which statement about its graph is correct?HardLevel 33If (p(x)=x+r) and (q(x)=x-r), what is (p(x)+q(x))?HardLevel 33If (p(x)=x+r) and (q(x)=x-r), what type of polynomial is (p(x)-q(x))?HardLevel 33If p(x) = 2x − 5, what is the value of p(p(3))?MediumLevel 33If (p(x)=3x+1), what is the value of (p(p(2)))?HardLevel 33For which value will the zero of ((n-1)x+n+2) be (1)?HardLevel 33If \(p(x)=\frac{x}{3}+a\) and \(p(6)=5\), what is the value of (a)?HardLevel 33In which option is p(x) − q(x) a linear polynomial?MediumLevel 33If (p(x)=2x+a) and (q(x)=x-3), what is (a) if the zero of (p(x)+q(x)) is (1)?HardLevel 33For which value will the zero of (p(x)=(c+1)x+2c) be (-4)?HardLevel 33If the zero of (p(x)=(c+1)x+2c) is (-4), what is the correct value of (c)?HardLevel 33If (p(x)=rx+5) and (p(2)=15), what is the value of (p(-1))?HardLevel 33