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Subjects

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 expression is a polynomial in x but not quadratic in x?MediumLevel 48If p(x) = 2x² − 5x + c and p(4) = 7, what is the value of c?MediumLevel 48For p(x) = x³ − 2x² − 5x + 6, which value makes p(x) = 0?MediumLevel 48If p(x) = ax² + 4x − 12 and x = 2 is a zero, what is a?MediumLevel 48In p(x) = 3x³ − 7x² + 2x − 11, what is the sum of the coefficient of x² and the constant term?EasyLevel 48What is the expanded polynomial form of \((2x+3)^2\)?MediumLevel 48If (p(x)=x^2-10x+21), what is the value of (p(7))?MediumLevel 48If the degree of (p(x)=(a-5)x^5+2x^3-7x+4) is (3), what is (a)?HardLevel 47If \(p(x)=kx^2-5x+6\) and \(p(-1)=14\), what is the value of \(k\)?HardLevel 47What is the coefficient of x² in the sum of the polynomials p(x) = 3x³ − 2x² + 5x − 1 and q(x) = −x³ + 7x² − 4x + 6?HardLevel 47What is the degree of the sum of (p(x)=4x^4-3x^2+2) and (q(x)=-4x^4+5x^3+x-8)?HardLevel 47If the degree of (p(x)) is (4) and the degree of (q(x)) is (3), what will generally be the degree of (p(x)q(x))?HardLevel 47What is the coefficient of (x^2) in ((x-2)(3x^2+4x-5))?HardLevel 47If \(x=3\) is a zero of the polynomial \(p(x)=x^2-kx+12\), what is the value of \(k\)?HardLevel 47For the polynomial p(x) = 2x³ − 9x² + 12x − 5, what is the value of p(2)?HardLevel 47For the polynomial \(p(x)=x^3-4x^2+mx+6\), what value of \(m\) will make \(p(1)=0\)?HardLevel 47If p(x) = x^4 - 2x^2 + 1, what is the value of p(-1)?HardLevel 47If p(x)=x²+ax+b, p(1)=0, and p(2)=0, what is a+b?MediumLevel 47Which of the following expressions is a polynomial in x of degree 5?HardLevel 47Which expression is not a polynomial in (x) though it looks similar to a quadratic?HardLevel 47