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)=ax-6) and (p(2)=p(5)-9), what is (a)?HardLevel 33In which option is a polynomial called linear even though the coefficient of (x) is (0)?HardLevel 33If (p(x)=2x-7), what is (a) when (p(a)=a)?HardLevel 33If (p(x)=mx+n), (p(0)=4) and (p(2)=10), what is (m+n)?HardLevel 33If (p(x)=mx+n), (p(1)=5) and (p(3)=13), what is (m)?HardLevel 33Which option has (p(2)=0) and (p(x)) is linear?HardLevel 33If (p(x)=3x-4), what is (p(x)+p(-x))?HardLevel 33If (p(x)=3x-4), what is (p(x)-p(-x))?HardLevel 33For which value will the zero of ((s-2)x+s) be (0)?HardLevel 33If (p(x)=2x+a) and (q(x)=4x-a), what is (a) if the zero of (p(x)+q(x)) is (-1)?HardLevel 33If (p(x)=2x+a) and (q(x)=4x-a), what is (p(x)-q(x))?HardLevel 33If (p(x)=ax+1) and (p(p(0))=7), what is (a)?HardLevel 33If (p(x)=x+a) and (p(p(0))=0), what is the value of (a)?HardLevel 33If (p(x)=mx+n) and (p(1)=p(2)), when can (p(x)) be linear?HardLevel 33If \(p(x)=ax+b\), where \(a\ne 0\), which statement about the zeroes of this linear polynomial is always true?HardLevel 33If (p(x)=7x-2), what is (p(x+2)-p(x-1))?HardLevel 33If (p(x)=2x-5), what is the correct value of (p(p(3)))?HardLevel 33After simplifying (6(3x-2)-4(4x+5)), which polynomial is obtained?HardLevel 34A student says that \(p(x)=\frac{6x^2-18x}{3x}\) is a linear polynomial because it can be written as \(2x-6\). Which statement is correct?HardLevel 34If the zero of (p(x)=(k+3)x-12) is (4), what is the value of (k)?HardLevel 34