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
Which of the following polynomials has (-2) as its leading coefficient?EasyLevel 47If the degree of (p(x)=(m-2)x^3+4x^2-7) is (2), what will be the value of (m)?MediumLevel 46What is the value of (p(0)+p(1)) for (p(x)=2x^3-5x^2+7x-4)?MediumLevel 46Which value gives (0) for the polynomial (p(x)=x^3-3x^2+3x-1)?MediumLevel 46If p(x) = kx^2 + 6x + 9 and p(-3) = 0, what is k?MediumLevel 47A student says that \(3x^2-5x+7\) is not a polynomial in one variable because it has three terms. What is the correct evaluation of the student's statement?EasyLevel 47If (x=2) is a zero of (p(x)=3x^2+bx-10), what will be the value of (b)?MediumLevel 46If \(p(x)=ax^2+3x+5\) has degree 1, what is the value of \(a\)?MediumLevel 47In the polynomial \\(4x^3-2x^2+7x-9\\), what is the sum of the coefficient of \\(x^2\\) and the constant term?MediumLevel 47If \(q(x)=x^2-kx+6\) satisfies \(q(2)=0\), what is the value of \(k\)?MediumLevel 47Which of the following expression is not a polynomial in (x)?MediumLevel 47If the coefficient of \(x^2\) in the polynomial \(p(x)=2x^3+mx^2-x+4\) is \(-5\), what is the value of \(m\)?MediumLevel 47What is the coefficient of the missing \(x^3\) term in the polynomial \(7x^5-3x^4+x^2-11\)?MediumLevel 47If \(f(x)=x^2+2x-8\), which of the following numbers is a zero of \(f(x)\)?MediumLevel 47If \(p(x)=3x^2-2x+1\), what is the value of \(p(2)-p(1)\)?MediumLevel 47If 2x^2 + 5x - 3 is written in descending powers, which is the leading term?EasyLevel 47For which value of \(a\) will the polynomial \(p(x)=(a-2)x^3+4x^2+1\) have degree 2?MediumLevel 47In which of the following polynomials is the coefficient of \(x\) zero?MediumLevel 47If \(r(x)=x^3-4x\), what is the value of \(r(-2)\)?MediumLevel 47Which statement is correct about the polynomial \(5x^2-3x+7\)?MediumLevel 47