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 the coefficient of
x
in the polynomial
p(x)=2x^2+kx+8
is 5, what is the value of
k
?MediumLevel 46If \(p(x)=x^2-9\), what is the value of \(p(3)\)?MediumLevel 46For which of the following polynomials is \(x=2\) a zero?MediumLevel 46For the polynomial \(p(x)=x^2+2x-8\), what is the value of \(p(2)\)?MediumLevel 46If \(a\ne0\) in the linear polynomial \(ax+b\), what is its degree?MediumLevel 46What is the leading coefficient of the polynomial \(p(y)=9y^4-y^2+5y-6\)?MediumLevel 46What is the coefficient of the \\(x^3\\) term in the polynomial \\(p(x)=4x^3-2x^2+7x-1\\)?MediumLevel 46Which polynomial is written in standard form with descending powers?EasyLevel 46If \(p(x)=3x^2-4x+1\) and \(q(x)=x^2+2x-5\), what is the value of \(p(x)+q(x)\)?MediumLevel 46If \(r(x)=2x^2-x+4\) is subtracted from \(p(x)=5x^2+3x-2\), which polynomial is obtained?MediumLevel 46What is the simplest form of the expression \(2x(3x^2-5x+1)\)?MediumLevel 46What is the expanded polynomial form of (x+3)(x-4)?MediumLevel 46Which polynomial is obtained by simplifying (2x-1)(x+5)?MediumLevel 46If \(p(x)=x^3-6x^2+11x-6\), what is the value of \(p(1)\)?MediumLevel 46If \(p(x)=x^2+kx+6\) and \(p(2)=0\), what is the value of \(k\)?MediumLevel 46If \(p(x)=x^2-ax+10\) and \(p(5)=0\), what is the value of \(a\)?MediumLevel 46For which value of \(m\) will \(x=1\) be a zero of the polynomial \(x^2-4x+m\)?MediumLevel 46Which conclusion is correct when x = 1 is substituted in the polynomial p(x) = 2x^2 - 3x + 1?MediumLevel 46If (p(x)=x^2+4x+4 ), what is the value of (p(-2) )?MediumLevel 46Which of the following expressions is a polynomial in one variable but not a quadratic polynomial?MediumLevel 46