Mathematics
Polynomials in one variable
एक चर वाले बहुपद
In this Class 10 Mathematics topic from the chapter “Polynomials,” students study algebraic expressions involving a single variable, such as x. They learn to identify a polynomial and its degree, understand constant, linear, quadratic, and cubic forms, and find its zeroes or roots. The topic also develops understanding of the relationship between zeroes and coefficients, helping students interpret polynomial equations and solve related problems accurately.
Practice questions
If p(x)=4x^2-3x+2, what is p(x)+p(-x)?MediumLevel 48If p(x)=2x³−8x, what is the value of p(−2)+p(2)?HardLevel 48Which of the following polynomials has exactly two distinct real zeroes, one of which has multiplicity 2?HardLevel 48If \(x\) is a real number, what is the minimum value of \(p(x)=x^2+10x+29\)?HardLevel 48If \(p(x)=x^2+kx+16\) is a perfect-square polynomial and \(k<0\), what is the value of \(k\)?HardLevel 48If \(p(x)=x^3+3x^2+3x+1\), what is the value of \(p(-2)\)?HardLevel 48For the polynomial \(p(x)=x^3-2x^2-3x+4\), what is the product of \(p(1)\) and \(p(-1)\)?HardLevel 48For p(x)=x^3+2x^2-4x-8, what is p(2)-p(-2)?MediumLevel 48If the polynomial \(f(x)=x^2+ax+b\) satisfies \(f(0)=-8\) and \(f(4)=0\), what is the value of \(a\)?HardLevel 48If \(p(x)=x^4+ax^2+b\) and \(p(0)=0\), which of the following conclusions is certainly true?HardLevel 48Which polynomial makes x=0 a zero?EasyLevel 48If \(p(x)=x^2+4x+6\), what is the simplified form of \(p(x-1)\)?HardLevel 48If \(p(x)=3x^2-2x+5\), what is the simplified form of \(p(2x)\)?HardLevel 48If \(p(x)=x^2-6x+5\), what is the value of \(p(x)-p(1)\)?HardLevel 48If (p(x)=ax^2+bx+c) with (a\neq0) and (p(1)=p(-1)=0), what is the value of (b)?ExpertLevel 46If (x-2) is a factor of (p(x)=x^3+kx^2-4x-4), what is the value of (k)?ExpertLevel 46If (p(x)=2x^3-5x^2+mx+6) leaves remainder (0) when divided by (x+1), what is (m)?ExpertLevel 46If (p(x)=x^4-5x^2+4), what is the degree of (p(x))?ExpertLevel 46If (p(x)=3x^2-7x+5), what is the value of (p(2)-p(1))?ExpertLevel 46If (p(x)=kx^3+2x^2-3x+1) is actually a quadratic polynomial, what must be the value of (k)?ExpertLevel 46